Applied Calculus for the Managerial, Life, and Social Sciences 10th Edition by Soo T. Tan - Test Bank Instant Download - Complete Test Bank With Answers Sample Questions Are Posted Below 1. Find the indefinite integral. a. b. c. d. ANSWER: a POINTS: 1 QUESTION TYPE: …
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Applied Calculus for the Managerial, Life, and Social Sciences 10th Edition by Soo T. Tan – Test Bank
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Sample Questions Are Posted Below
| 1. Find the indefinite integral.
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| 2. Find the indefinite integral.
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| 3. Find the indefinite integral.
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| 4. Find the indefinite integral.
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| 5. Find the indefinite integral.
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| 6. Find the indefinite integral.
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| 7. Find the indefinite integral.
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| 8. Find the indefinite integral.
Hint:
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| 9. Find the indefinite integral.
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| 10. Find the indefinite integral.
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| 11. Find the indefinite integral.
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| 12. Find the indefinite integral.
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| 13. Find by solving the initial value problem.
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| 14. Find f (x) by solving the initial value problem.
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| 15. Find by solving the initial value problem.
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| 16. Find the function f given that the slope of the tangent line to the graph of f at any point is and that the graph of f passes through the given point.
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| 17. Find the function f given that the slope of the tangent line to the graph of f at any point is and that the graph of f passes through the given point.
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| 18. Lorimar Watch Company manufactures travel clocks. The daily marginal cost function associated with producing these clocks is
where is measured in dollars/unit and x denotes the number of units produced. Management has determined that the daily fixed cost incurred in producing these clocks is $130. Find the total cost incurred by Lorimar in producing the first 600 travel clocks/day.
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| 19. Lorimar Watch Company manufactures travel clocks. The daily marginal cost function associated with producing these clocks is
where is measured in dollars/unit and x denotes the number of units produced. Management has determined that the daily fixed cost incurred in producing these clocks is $130. Find the total cost incurred by Lorimar in producing the first 400 travel clocks/day.
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| 20. As part of a quality-control program, the chess sets manufactured by Jones Brothers are subjected to a final inspection before packing. The rate of increase in the number of sets checked per hour by an inspector t hours into the 8 A.M. to 12 noon morning shift is approximately
How many sets does the average inspector check during a morning shift? (Hint: .)
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| 21. The temperature on a certain day as measured at the airport of a city is changing at the rate of
F/hr, where t is measured in hours, with corresponding to 6 a.m. The temperature at 6 a.m. was 23F. What was the temperature at 9 a.m.? Please round your answer to whole degrees.
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| 22. A study conducted by TeleCable estimates that the number of cable TV subscribers will grow at the rate of
new subscribers/month t months from the start date of the service. If 8,000 subscribers signed up for the service before the starting date, how many subscribers will there be 16 months from that date?
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| 23. The velocity, in feet/second, of a rocket t seconds into vertical flight is given by
What is the altitude of the rocket 20 seconds after liftoff? Hint: ; .
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| 24. A car traveling along a straight road at 50 ft/sec accelerated to a speed of 80 ft/sec over a distance of 500 ft. What was the acceleration of the car, assuming it was constant?
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| 25. Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false.
If f and g are integrable, then .
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| 26. Lorimar Watch Company manufactures travel clocks. The daily marginal cost function associated with producing these clocks is
where C ‘(x) is measured in dollars/unit and x denotes the number of units produced. Management has determined that the daily fixed cost incurred in producing these clocks is $110. Find the total cost incurred by Lorimar in producing the first 200 travel clocks/day. $__________
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| 27. Lorimar Watch Company manufactures travel clocks. The daily marginal cost function associated with producing these clocks is
where is measured in dollars/unit and x denotes the number of units produced. Management has determined that the daily fixed cost incurred in producing these clocks is $130. Find the total cost incurred by Lorimar in producing the first 500 travel clocks/day. $__________
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| 28. As part of a quality-control program, the chess sets manufactured by Jones Brothers are subjected to a final inspection before packing. The rate of increase in the number of sets checked per hour by an inspector t hours into the 8 A.M. to 10 morning shift is approximately
How many sets does the average inspector check during a morning shift? (Hint: .) __________ sets
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| 29. A study conducted by TeleCable estimates that the number of cable TV subscribers will grow at the rate of
new subscribers/month t months from the start date of the service. If 4,000 subscribers signed up for the service before the starting date, how many subscribers will there be 16 months from that date? __________ subscribers
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| 30. The velocity, in feet/second, of a rocket t seconds into vertical flight is given by
What is the altitude of the rocket 30 seconds after liftoff? Hint: ; . __________ ft
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| 31. A car traveling along a straight road at 70 ft/sec accelerated to a speed of 98 ft/sec over a distance of 480 ft. What was the acceleration of the car, assuming it was constant?
__________
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| 32. Find the indefinite integral.
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| 33. Find the indefinite integral.
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| 34. Find the indefinite integral.
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| 35. Find the indefinite integral.
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| 36. Find the indefinite integral.
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| 37. Find the indefinite integral.
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| 38. Find the indefinite integral.
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| 39. Find the indefinite integral.
Hint:
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| 40. Find the indefinite integral.
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| 41. Find the indefinite integral.
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| 42. Find the indefinite integral.
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| 43. Find the indefinite integral.
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| 44. Find by solving the initial value problem.
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| 45. Find by solving the initial value problem.
;
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| 46. Find by solving the initial value problem.
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| 47. Find the function f given that the slope of the tangent line to the graph of f at any point is and that the graph of f passes through the given point.
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| 48. Find the function f given that the slope of the tangent line to the graph of f at any point is and that the graph of f passes through the given point.
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| 49. Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false.
If f and g are integrable, then .
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| 1. Find the indefinite integral.
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| 2. Find the indefinite integral.
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| 3. Find the indefinite integral.
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| 4. Find the indefinite integral.
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| 5. Find the indefinite integral.
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| 6. Find the indefinite integral.
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| 7. Find the indefinite integral.
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| 8. Find the indefinite integral.
Hint:
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| 9. Find the indefinite integral.
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| 10. Find the indefinite integral.
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| 11. Find the indefinite integral.
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| 12. Find the indefinite integral.
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| 13. Find by solving the initial value problem.
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| 14. Find f (x) by solving the initial value problem.
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| 15. Find by solving the initial value problem.
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| 16. Find the function f given that the slope of the tangent line to the graph of f at any point is and that the graph of f passes through the given point.
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| 17. Find the function f given that the slope of the tangent line to the graph of f at any point is and that the graph of f passes through the given point.
;
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| 18. Lorimar Watch Company manufactures travel clocks. The daily marginal cost function associated with producing these clocks is
where is measured in dollars/unit and x denotes the number of units produced. Management has determined that the daily fixed cost incurred in producing these clocks is $130. Find the total cost incurred by Lorimar in producing the first 600 travel clocks/day.
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| 19. Lorimar Watch Company manufactures travel clocks. The daily marginal cost function associated with producing these clocks is
where is measured in dollars/unit and x denotes the number of units produced. Management has determined that the daily fixed cost incurred in producing these clocks is $130. Find the total cost incurred by Lorimar in producing the first 400 travel clocks/day.
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| 20. As part of a quality-control program, the chess sets manufactured by Jones Brothers are subjected to a final inspection before packing. The rate of increase in the number of sets checked per hour by an inspector t hours into the 8 A.M. to 12 noon morning shift is approximately
How many sets does the average inspector check during a morning shift? (Hint: .)
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| 21. The temperature on a certain day as measured at the airport of a city is changing at the rate of
F/hr, where t is measured in hours, with corresponding to 6 a.m. The temperature at 6 a.m. was 23F. What was the temperature at 9 a.m.? Please round your answer to whole degrees.
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| 22. A study conducted by TeleCable estimates that the number of cable TV subscribers will grow at the rate of
new subscribers/month t months from the start date of the service. If 8,000 subscribers signed up for the service before the starting date, how many subscribers will there be 16 months from that date?
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| 23. The velocity, in feet/second, of a rocket t seconds into vertical flight is given by
What is the altitude of the rocket 20 seconds after liftoff? Hint: ; .
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| 24. A car traveling along a straight road at 50 ft/sec accelerated to a speed of 80 ft/sec over a distance of 500 ft. What was the acceleration of the car, assuming it was constant?
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| 25. Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false.
If f and g are integrable, then .
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| 26. Lorimar Watch Company manufactures travel clocks. The daily marginal cost function associated with producing these clocks is
where C ‘(x) is measured in dollars/unit and x denotes the number of units produced. Management has determined that the daily fixed cost incurred in producing these clocks is $110. Find the total cost incurred by Lorimar in producing the first 200 travel clocks/day. $__________
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| 27. Lorimar Watch Company manufactures travel clocks. The daily marginal cost function associated with producing these clocks is
where is measured in dollars/unit and x denotes the number of units produced. Management has determined that the daily fixed cost incurred in producing these clocks is $130. Find the total cost incurred by Lorimar in producing the first 500 travel clocks/day. $__________
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| 28. As part of a quality-control program, the chess sets manufactured by Jones Brothers are subjected to a final inspection before packing. The rate of increase in the number of sets checked per hour by an inspector t hours into the 8 A.M. to 10 morning shift is approximately
How many sets does the average inspector check during a morning shift? (Hint: .) __________ sets
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| 29. A study conducted by TeleCable estimates that the number of cable TV subscribers will grow at the rate of
new subscribers/month t months from the start date of the service. If 4,000 subscribers signed up for the service before the starting date, how many subscribers will there be 16 months from that date? __________ subscribers
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| 30. The velocity, in feet/second, of a rocket t seconds into vertical flight is given by
What is the altitude of the rocket 30 seconds after liftoff? Hint: ; . __________ ft
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| 31. A car traveling along a straight road at 70 ft/sec accelerated to a speed of 98 ft/sec over a distance of 480 ft. What was the acceleration of the car, assuming it was constant?
__________
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| 32. Find the indefinite integral.
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| 33. Find the indefinite integral.
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| 34. Find the indefinite integral.
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| 35. Find the indefinite integral.
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| 36. Find the indefinite integral.
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| 37. Find the indefinite integral.
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| 38. Find the indefinite integral.
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| 39. Find the indefinite integral.
Hint:
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| 40. Find the indefinite integral.
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| 41. Find the indefinite integral.
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| 42. Find the indefinite integral.
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| 43. Find the indefinite integral.
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| 44. Find by solving the initial value problem.
;
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| 45. Find by solving the initial value problem.
;
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| 46. Find by solving the initial value problem.
;
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| 47. Find the function f given that the slope of the tangent line to the graph of f at any point is and that the graph of f passes through the given point.
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| 48. Find the function f given that the slope of the tangent line to the graph of f at any point is and that the graph of f passes through the given point.
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| 49. Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false.
If f and g are integrable, then .
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| 1. Find an approximation of the area of the region R under the graph of f by computing the Riemann sum of f corresponding to the partition of the interval into the subintervals shown in the accompanying figures. Use the midpoints of the subintervals as the representative points. Round your answer to the nearest hundredth.
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| 2. Let
Sketch the region R under the graph of f on the interval [0, 2] and find its exact area using geometry.
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| 3. Find an approximation of the area of the region R under the graph of f by computing the Riemann sum of f corresponding to the partition of the interval into the subintervals shown in the accompanying figures. Use the midpoints of the subintervals as the representative points.
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| 4. Let
Use a Riemann sum with four subintervals of equal length () to approximate the area of R (under the graph of f on the interval [0, 2]). Choose the representative points to be the left end points of the subintervals. Repeat previous part with eight subintervals of equal length (). Compare the approximations obtained in previous parts with the exact area (14 sq units). Do the approximations improve with larger n?
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| 5. Let . Sketch the region R under the graph of f on the interval [0, 4], and use a Riemann sum with four subintervals of equal length to approximate the area of R. Choose the representative points to be the right endpoints of the subintervals.
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| 6. Let
Sketch the region R under the graph of f on the interval [0, 2] and find its exact area using geometry.
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| 7. Let
Use a Riemann sum with four subintervals of equal length () to approximate the area of R (under the graph of f on the interval [0, 2]). Choose the representative points to be the left end points of the subintervals. Repeat previous part with eight subintervals of equal length (). Compare the approximations obtained in previous parts with the exact area (4 sq units). Do the approximations improve with larger n?
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| 8. Let . Sketch the region R under the graph of f on the interval [0, 3], and use a Riemann sum with five subintervals of equal length to approximate the area of R. Choose the representative points to be the right endpoints of the subintervals.
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| 9. Let and compute the Riemann sum of f over the interval , choosing the representative points to be the midpoints of the subintervals, using five subintervals of equal length ().
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| 10. Let and compute the Riemann sum of f over the interval , choosing the representative points to be the left endpoints of the subintervals, using five subintervals of equal length .
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| 11. Let and compute the Riemann sum of f over the interval , using
Two subintervals of equal length (). Five subintervals of equal length (). Ten subintervals of equal length (). In each case, choose the representative points to be the right end points of the subintervals.
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| 12. Let and compute the Riemann sum of f over the interval , using
Two subintervals of equal length (). Five subintervals of equal length (). Ten subintervals of equal length (). In each case, choose the representative points to be the midpoints of the subintervals.
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| 13. Let and compute the Riemann sum of f over the interval , choosing the representative points to be the left endpoints of the subintervals, using two subintervals of equal length .
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| 14. Let and compute the Riemann sum of f over the interval , using
Two subintervals of equal length (). Five subintervals of equal length (). Ten subintervals of equal length (). In each case, choose the representative points to be the right end points of the subintervals. Round your answer to two decimal places.
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| 15. Find an approximation of the area of the region R under the graph of the function f on the interval [a, b]. Use n subintervals and choose the representative points as indicated. Round your answer to two decimal points.
; [0, 2]; ; midpoints.
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| 16. Find an approximation of the area of the region R under the graph of the function f on the interval [a, b]. Use n subintervals and choose the representative points as indicated.
; ; ; left end points
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| 17. Find an approximation of the area of the region R under the graph of the function f on the interval [a, b]. Use n subintervals and choose the representative points as indicated.
; [1, 3]; ; right end points
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| 18. Find an approximation of the area of the region R under the graph of the function f on the interval [a, b]. Use n subintervals and choose the representative points as indicated. Please round your answer to two decimal places.
; ; ; midpoints
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| 19. Figure (a) shows a vacant lot with a 100-ft frontage in a development. To estimate its area, we introduce a coordinate system so that the x-axis coincides with the edge of the straight road forming the lower boundary of the property, as shown in Figure (b). Then, thinking of the upper boundary of the property as the graph of a continuous function f over the interval [0, 100], we see that the problem is mathematically equivalent to that of finding the area under the graph of f on [0, 100]. To estimate the area of the lot using a Riemann sum, we divide the interval [0, 100] into five equal subintervals of length 20 ft. Then, using surveyor’s equipment, we measure the distance from the midpoint of each of these subintervals to the upper boundary of the property. These measurements give the values of f(x) at x = 10, 30, 50, 70, and 90. What is the approximate area of the lot?
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| 20. Figure (a) shows a vacant lot with a 80-ft frontage in a development. To estimate its area, we introduce a coordinate system so that the x-axis coincides with the edge of the straight road forming the lower boundary of the property, as shown in Figure (b). Then, thinking of the upper boundary of the property as the graph of a continuous function f over the interval [0, 80], we see that the problem is mathematically equivalent to that of finding the area under the graph of f on [0, 80]. To estimate the area of the lot using a Riemann sum, we divide the interval [0, 80] into four equal subintervals of length 20 ft. Then, using surveyor’s equipment, we measure the distance from the midpoint of each of these subintervals to the upper boundary of the property. These measurements give the values of f(x) at x = 10, 30, 50, and 70. What is the approximate area of the lot?
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| 21. Find an approximation of the area of the region R under the graph of f by computing the Riemann sum of f corresponding to the partition of the interval into the subintervals shown in the accompanying figures. Use the midpoints of the subintervals as the representative points. Round your answer to the nearest hundredth.
__________ sq units
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| 22. Find an approximation of the area of the region R under the graph of f by computing the Riemann sum of f corresponding to the partition of the interval into the subintervals shown in the accompanying figures. Use the midpoints of the subintervals as the representative points.
__________ sq units
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| 23. Find an approximation of the area of the region R under the graph of the function f on the interval [a, b]. Use n subintervals and choose the representative points as indicated. Round to two decimal places.
; [0, 2]; ; midpoints __________ sq units
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| 24. Find an approximation of the area of the region R under the graph of the function f on the interval [a, b]. Use n subintervals and choose the representative points as indicated. Round to three decimal places.
; ; ; left end points __________ sq units
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| 25. Find an approximation of the area of the region R under the graph of the function f on the interval [a, b]. Use n subintervals and choose the representative points as indicated.
; [1, 3]; ; right end points __________ sq units
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| 26. Find an approximation of the area of the region R under the graph of the function f on the interval [a, b]. Use n subintervals and choose the representative points as indicated. Please round your answer to two decimal places.
; ; ; midpoints __________sq units
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| 27. Figure (a) shows a vacant lot with a 100-ft frontage in a development. To estimate its area, we introduce a coordinate system so that the x-axis coincides with the edge of the straight road forming the lower boundary of the property, as shown in Figure (b). Then, thinking of the upper boundary of the property as the graph of a continuous function f over the interval [0, 100], we see that the problem is mathematically equivalent to that of finding the area under the graph of f on [0, 100]. To estimate the area of the lot using a Riemann sum, we divide the interval [0, 100] into five equal subintervals of length 20 ft. Then, using surveyor’s equipment, we measure the distance from the midpoint of each of these subintervals to the upper boundary of the property. These measurements give the values of f(x) at x = 10, 30, 50, 70, and 90. What is the approximate area of the lot?
__________ square feet
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| 28. Figure (a) shows a vacant lot with a 80-ft frontage in a development. To estimate its area, we introduce a coordinate system so that the x-axis coincides with the edge of the straight road forming the lower boundary of the property, as shown in Figure (b). Then, thinking of the upper boundary of the property as the graph of a continuous function f over the interval [0, 80], we see that the problem is mathematically equivalent to that of finding the area under the graph of f on [0, 80]. To estimate the area of the lot using a Riemann sum, we divide the interval [0, 80] into four equal subintervals of length 20 ft. Then, using surveyor’s equipment, we measure the distance from the midpoint of each of these subintervals to the upper boundary of the property. These measurements give the values of f(x) at x = 10, 30, 50, and 70. What is the approximate area of the lot?
__________ square feet
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| 29. Let
Use a Riemann sum with four subintervals of equal length to approximate the area of R (under the graph of f on the interval [0, 2]). Choose the representative points to be the left end points of the subintervals. __________ sq units Repeat previous part with eight subintervals of equal length . __________ sq units Compare the approximations obtained in previous parts with the exact area (14 sq units). Do the approximations improve with larger n?
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| 30. Let
Use a Riemann sum with four subintervals of equal length to approximate the area of R (under the graph of f on the interval [0, 2]). Choose the representative points to be the left end points of the subintervals. __________ sq units Repeat previous part with eight subintervals of equal length . __________ sq units Compare the approximations obtained in previous parts with the exact area (12 sq units). Do the approximations improve with larger n?
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| 31. Let and compute the Riemann sum of f over the interval , choosing the representative points to be the midpoints of the subintervals, using:
Two subintervals of equal length . __________ sq units Five subintervals of equal length . __________ sq units Ten subintervals of equal length . __________ sq units Can you guess at the area of the region under the graph of f on the interval ? ≈ __________sq units
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| 32. Let and compute the Riemann sum of f over the interval , choosing the representative points to be the left endpoints of the subintervals, using:
Two subintervals of equal length . __________ sq units Five subintervals of equal length . __________ sq units Ten subintervals of equal length . __________ sq units Can you guess at the area of the region under the graph of f on the interval ? Round your answer to the nearest tenths. ≈ __________ sq units
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| 33. Let and compute the Riemann sum of f over the interval [3, 5] , using
Two subintervals of equal length . Choose the representative points to be the right end points of the subintervals. __________ sq units Five subintervals of equal length . Choose the representative points to be the right end points of the subintervals. __________ sq units Ten subintervals of equal length . Choose the representative points to be the right end points of the subintervals. __________ sq units
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| 34. Let and compute the Riemann sum of f over the interval [3, 4] , using
Two subintervals of equal length . Choose the representative points to be the midpoints of the subintervals. __________ sq units Five subintervals of equal length . Choose the representative points to be the midpoints of the subintervals. __________ sq units Ten subintervals of equal length . Choose the representative points to be the midpoints of the subintervals. __________ sq units
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| 35. Let and compute the Riemann sum of f over the interval , choosing the representative points to be the left endpoints of the subintervals, using:
Two subintervals of equal length . __________ sq units Five subintervals of equal length . __________ sq units Ten subintervals of equal length . __________ sq units Can you guess at the area of the region under the graph of f on the interval ? ≈ __________ sq units
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| 36. Let and compute the Riemann sum of f over the interval [3, 4] , using
Two subintervals of equal length . Choose the representative points to be the right end points of the subintervals. __________ sq units Five subintervals of equal length . Choose the representative points to be the right end points of the subintervals. __________ sq units Ten subintervals of equal length . Choose the representative points to be the right end points of the subintervals. __________ sq units
|
| 1. Find the area of the region under the graph of the function
on the interval , using the fundamental theorem of calculus. Then verify your result using geometry.
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| 2. Find the area of the region under the graph of the function
on the interval , using the fundamental theorem of calculus. Then verify your result using geometry.
|
| 3. Find the area of the region under the graph of the function
on the interval .
|
| 4. Find the area of the region under the graph of the function
on the interval .
|
| 5. Find the area of the region under the graph of the function
on the interval .
|
| 6. Find the area of the region under the graph of the function
on the interval .
|
| 7. Find the area of the region under the graph of the function on the interval .
;
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| 8. Evaluate the definite integral.
|
| 9. Evaluate the definite integral.
|
| 10. Evaluate the definite integral.
|
| 11. Evaluate the definite integral.
|
| 12. Evaluate the definite integral.
|
| 13. Evaluate the definite integral.
|
| 14. Evaluate the definite integral.
|
| 15. Evaluate the definite integral.
|
| 16. Evaluate the definite integral.
|
| 17. Evaluate the definite integral.
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| 18. Evaluate the definite integral.
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| 19. A division of Ditton Industries manufactures a deluxe toaster oven. Management has determined that the daily marginal cost function associated with producing these toaster ovens is given by
where is measured in dollars/unit and denotes the number of units produced. Management has also determined that the daily fixed cost incurred in the production is $800. Find the total cost incurred by Ditton in producing the first 500 units of these toaster ovens per day. What is the total cost incurred by Ditton in producing the 401st through 500th units/day?
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| 20. Tempco Electronics, a division of Tempco Toys, manufactures an electronic football game. An efficiency study showed that the rate at which the games are assembled by the average worker t hours after starting work at 8 a.m. is
units/hour. How many units can the average worker be expected to assemble in the first hour of the morning shift? Answers are rounded to the nearest whole unit.
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| 21. In a recent pretrial run for the world water speed record, the velocity of the Sea Falcon II seconds after firing the booster rocket was given by
ft/sec. Find the distance covered by the boat over the 10-second period after the booster rocket was activated. Hint: The distance is given by .
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| 22. Annual sales (in millions of units) of hand-held computers are expected to grow in accordance with the function
where is measured in years, with corresponding to 1997. How many hand-held computers will be sold over the 6-year period between the beginning of 1997 and the end of 2002?
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| 23. The number of Americans aged 45 to 54 (which stood at 25 million at the beginning of 1990) grew at the rate of
million people/year, years from the beginning of 1990. How many Americans aged 45 to 54 were added to the population between 1990 and the year 1999? Give your answer to one decimal place.
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| 24. The population aged 65 years old and older (in millions) from 2000 to 2050 is projected to be
where is measured in decades, with corresponding to 2000. What will be the average population aged 65 years and older over the years from 2000 to 2020? (Hint: The average population is given by . Multiply the integrand by and then use the method of substitution.) Round your answer to one decimal place.
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| 25. Find the area of the region under the graph of the function
on the interval , using the fundamental theorem of calculus. Then verify your result using geometry.
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| 26. Find the area of the region under the graph of the function
on the interval .
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| 27. Evaluate the definite integral.
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| 28. Evaluate the definite integral.
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| 29. Annual sales (in millions of units) of hand-held computers are expected to grow in accordance with the function
where is measured in years, with corresponding to 1997. How many hand-held computers will be sold over the 3-year period between the beginning of 1997 and the end of 1999? Round your answer to two decimal places, if necessary.
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| 30. The number of Americans aged 45 to 54 (which stood at 25 million at the beginning of 1990) grew at the rate of
million people/year, t years from the beginning of 1990. How many Americans aged 45 to 54 were added to the population between 1990 and the year 1998? Please give your answer to one decimal place.
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| 31. The population aged 65 years old and older (in millions) from 2000 to 2050 is projected to be
where is measured in decades, with corresponding to 2000. What will be the average population aged 65 years and older over the years from 2000 to 2040? (Hint: The average population is given by . Multiply the integrand by and then use the method of substitution.) Please round your answer to one decimal place. __________ million
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| 32. Find the area of the region under the graph of the function
on the interval , using the fundamental theorem of calculus. Then verify your result using geometry.
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| 33. Find the area of the region under the graph of the function
on the interval .
|
| 34. Find the area of the region under the graph of the function
on the interval .
|
| 35. Find the area of the region under the graph of the function
on the interval .
|
| 36. Find the area of the region under the graph of the function f on the interval .
;
|
| 37. Evaluate the definite integral.
|
| 38. Evaluate the definite integral.
|
| 39. Evaluate the definite integral.
|
| 40. Evaluate the definite integral.
|
| 41. Evaluate the definite integral.
|
| 42. Evaluate the definite integral.
|
| 43. Evaluate the definite integral.
|
| 44. Tempco Electronics, a division of Tempco Toys, manufactures an electronic football game. An efficiency study showed that the rate at which the games are assembled by the average worker t hours after starting work at 8 a.m. is
units/hour. Find the total number of games the average worker can be expected to assemble in the 4-hour morning shift. __________ units How many units can the average worker be expected to assemble in the first hour of the morning shift? Please round the answer to the nearest whole unit. __________ units In the second hour of the morning shift? Please round the answer to the nearest whole unit. __________ units
|
| 45. In a recent pretrial run for the world water speed record, the velocity of the Sea Falcon II t seconds after firing the booster rocket was given by
ft/sec. Find the distance covered by the boat over the 5-second period after the booster rocket was activated. Hint: The distance is given by .
|
| 46. Evaluate the definite integral.
|
| 47. Evaluate the definite integral.
|
| 1. The demand function for a certain make of replacement cartridges for a water purifier is given by
where p is the unit price in dollars and x is the quantity demanded each week, measured in units of a thousand. Determine the consumers’ surplus if the market price is set at $1/cartridge. Round your answer to the nearest dollar.
|
| 2. The demand function for a certain brand of compact disc is given by
where p is the wholesale unit price in dollars and x is the quantity demanded each week, measured in units of a thousand. Determine the consumers’ surplus if the wholesale market price is set at $1/disc. Round your answer to the nearest dollar.
|
| 3. It is known that the quantity demanded of a certain make of portable hair dryer is x hundred units/week and the corresponding wholesale unit price is
dollars. Determine the consumers’ surplus if the wholesale market price is set at $20/unit. Round your answer to the nearest dollar.
|
| 4. The demand function for a certain brand of compact disc is given by
The supply function for the compact discs of is given by where p is the wholesale unit price in dollars and x is the quantity demanded each week, measured in units of a thousand. Determine the producers’ surplus if the wholesale market price is set at the equilibrium price. Round your answer to the nearest dollar.
|
| 5. The management of the Titan Tire Company has determined that the quantity demanded x of their Super Titan tires/week is related to the unit price p by the relation
where p is measured in dollars and x is measured in units of a thousand. Titan will make x units of the tires available in the market if the unit price is dollars. Determine the consumers’ surplus and the producers’ surplus when the market unit price is set at the equilibrium price. Round your answers to the nearest dollar.
|
| 6. The quantity demanded x (in units of a hundred) of the miniature cameras per week is related to the unit price p (in dollars) by
and the quantity x (in units of a hundred) that the supplier is willing to make available in the market is related to the unit price p (in dollars) by If the market price is set at the equilibrium price, find the consumers’ surplus and the producers’ surplus. Please round the answers to the nearest dollar.
|
| 7. Find . Round your answer to the nearest integer.
|
| 8. Suppose an investment is expected to generate income at the rate of
dollars/year for the next 6 years. Find the present value of this investment if the prevailing interest rate is 4% /year compounded continuously. Round your answer to the nearest dollar.
|
| 9. A firm purchased a 15-year franchise for a computer outlet store that is expected to generate income at the rate of
dollars per year. If the prevailing interest rate is 9% per year compounded continuously, find the present value of the franchise.
|
| 10. Find the amount of an annuity if $200 per month is paid into it for a period of 17 years, earning interest at the rate of 7% per year compounded continuously. Round you answer to the nearest dollar.
|
| 11. Aiso deposits $130/month in a savings account paying 5% /year compounded continuously. Estimate the amount that will be in his account after 5 years. Round your answer to the nearest dollar.
|
| 12. The Armstrongs wish to establish a custodial account to finance their children’s education. If they deposit $100 monthly for 10 years in a savings account paying 6% /year compounded continuously, how much will their savings account be worth at the end of this period? Round your answer to the nearest dollar.
|
| 13. Estimate the present value of an annuity if payments are $700 monthly for 14 years and the account earns interest at the rate of 4% /year compounded continuously. Round your answer to the nearest dollar.
|
| 14. Estimate the present value of an annuity if payments are $1,500 monthly for 15 years and the account earns interest at the rate of 10% per year compounded continuously. Round your answer to the nearest dollar.
|
| 15. A state lottery commission pays the winner of the “Million Dollar” lottery 20 annual installments of $30,000 each. If the prevailing interest rate is 8% /year compounded continuously, find the present value of the winning ticket. Round your answer to the nearest dollar.
|
| 16. Sinclair wishes to supplement his retirement income by $250 per month for the next 12 years. He plans to obtain a reverse annuity mortgage (RAM) on his home to meet this need. Estimate the amount of the mortgage he will require if the prevailing interest rate is 11% per year compounded continuously.
|
| 17. A certain country’s income distribution is described by the function
Sketch the Lorentz curve for this function. Compute and interpret your results.
|
| 18. In a study conducted by a certain country’s Economic Development Board, it was found that the Lorentz curve for the distribution of income of college teachers was described by the function
and that of lawyers by the function Compute the coefficient of inequality for each Lorentz curve. Round your answer to four decimal places. Which profession has a more equitable income distribution?
|
| 19. A certain country’s income distribution is described by the function
Compute and .
|
| 20. In a study conducted by a certain country’s Economic Development Board, it was found that the Lorentz curve for the distribution of income of stockbrokers was described by the function
and that of high school teachers by the function Compute the coefficient of inequality for each Lorentz curve. Round your answers to the nearest hundredth. Which profession has a more equitable income distribution?
|
| 21. The demand function for a certain make of replacement cartridges for a water purifier is given by
where p is the unit price in dollars and x is the quantity demanded each week, measured in units of a thousand. Determine the consumers’ surplus if the market price is set at $1/cartridge. Round your answer to the nearest dollar. CS = $__________
|
| 22. The demand function for a certain brand of compact disc is given by
where p is the wholesale unit price in dollars and x is the quantity demanded each week, measured in units of a thousand. Determine the consumers’ surplus if the wholesale market price is set at $3/disc. Round your answer to the nearest dollar. $__________
|
| 23. It is known that the quantity demanded of a certain make of portable hair dryer is x hundred units/week and the corresponding wholesale unit price is
dollars. Determine the consumers’ surplus if the wholesale market price is set at $10/unit. Round your answer to the nearest dollar. $__________
|
| 24. The demand function for a certain brand of compact disc is given by
The supply function for the compact discs is given by where p is the wholesale unit price in dollars and x is the quantity demanded each week, measured in units of a thousand. Determine the producers’ surplus if the wholesale market price is set at the equilibrium price. Round your answer to the nearest dollar. $__________
|
| 25. Suppose an investment is expected to generate income at the rate of
dollars/year for the next 6 years. Find the present value of this investment if the prevailing interest rate is 0.04% /year compounded continuously. Round your answer to the nearest dollar. $__________
|
| 26. A firm purchased a 10-year franchise for a computer outlet store that is expected to generate income at the rate of
dollars per year. If the prevailing interest rate is 10% per year compounded continuously, find the present value of the franchise. Please round the answer to the nearest dollar. $__________
|
| 27. Find the amount of an annuity if $230 per month is paid into it for a period of 20 years, earning interest at the rate of 7% per year compounded continuously. Please round the answer to the nearest dollar.
$__________
|
| 28. Aiso deposits $150 / month in a savings account paying 8% /year compounded continuously. Estimate the amount that will be in his account after 25 years. Round your answer to the nearest dollar.
$__________
|
| 29. The Armstrongs wish to establish a custodial account to finance their children’s education. If they deposit $200 monthly for 10 years in a savings account paying 8% /year compounded continuously, how much will their savings account be worth at the end of this period? Round your answer to the nearest dollar.
$__________
|
| 30. Estimate the present value of an annuity if payments are $800 monthly for 19 years and the account earns interest at the rate of 8% /year compounded continuously. Round your answer to the nearest dollar.
$__________
|
| 31. Estimate the present value of an annuity if payments are $1,200 monthly for 11 years and the account earns interest at the rate of 10% per year compounded continuously. Please round the answer to the nearest dollar.
$__________
|
| 32. A state lottery commission pays the winner of the “Million Dollar” lottery 30 annual installments of $30,000 each. If the prevailing interest rate is 5% /year compounded continuously, find the present value of the winning ticket. Round your answer to the nearest dollar.
$__________
|
| 33. Sinclair wishes to supplement his retirement income by $400 per month for the next 14 years. He plans to obtain a reverse annuity mortgage (RAM) on his home to meet this need. Estimate the amount of the mortgage he will require if the prevailing interest rate is 11% per year compounded continuously. Please round the answer to the nearest dollar.
$__________
|
| 34. The management of the Titan Tire Company has determined that the quantity demanded x of their Super Titan tires/week is related to the unit price p by the relation
where p is measured in dollars and x is measured in units of a thousand. Titan will make x units of the tires available in the market if the unit price is dollars. Determine the consumers’ surplus and the producers’ surplus when the market unit price is set at the equilibrium price. Round your answers to the nearest dollars. CS = $__________ PS = $__________
|
| 35. The quantity demanded x (in units of a hundred) of the miniature cameras per week is related to the unit price p (in dollars) by
and the quantity x (in units of a hundred) that the supplier is willing to make available in the market is related to the unit price p (in dollars) by If the market price is set at the equilibrium price, find the consumers’ surplus and the producers’ surplus. Please round the answers to the nearest dollar. The consumers’ surplus: $__________ The producers’ surplus: $__________
|
| 36. In a study conducted by a certain country’s Economic Development Board, it was found that the Lorentz curve for the distribution of income of college teachers was described by the function
and that of lawyers by the function Compute the coefficient of inequality for each Lorentz curve. Round your answer to four decimal places. The coefficient of inequality for college teachers is __________. The coefficient of inequality for lawyers is __________. Which profession has a more equitable income distribution?
|
| 37. In a study conducted by a certain country’s Economic Development Board, it was found that the Lorentz curve for the distribution of income of stockbrokers was described by the function
and that of high school teachers by the function Compute the coefficient of inequality for each Lorentz curve. Round your answers to the nearest hundredth. The coefficient of inequality for stockbrokers is __________. The coefficient of inequality for teachers is __________. Which profession has a more equitable income distribution?
|
38. Verify that .
|
| 1. Evaluate the given definite integral.
|
| 2. Evaluate the given definite integral.
|
| 3. Evaluate the given definite integral.
|
| 4. Evaluate the given definite integral.
|
| 5. Evaluate the definite integral.
|
| 6. Evaluate the given definite integral.
|
| 7. Evaluate the given definite integral.
|
| 8. Evaluate the given definite integral.
|
| 9. Evaluate the definite integral.
|
| 10. Evaluate the given definite integral.
|
| 11. Evaluate the definite integral.
|
| 12. Evaluate the given definite integral.
|
| 13. Find the average value of the function
over the indicated interval .
|
| 14. Find the average value of the function
over the indicated interval .
|
| 15. Find the average value of the function
over the indicated interval .
|
| 16. Find the average value of the function
over the interval .
|
| 17. A bottle of white wine at room temperature (68°F) is placed in a refrigerator at 3 P.M. Its temperature after t hours is changing at the rate of -18e-0.6t °F/hr.
By how many degrees will the temperature of the wine have dropped by 12 P.M.? Please round your answer to one decimal place.
|
| 18. The net investment flow (rate of capital formation) of the giant conglomerate LTF incorporated is projected to be
million dollars/year in year t. Find the accruement on the company’s capital stock in the eight year. Hint: The amount is given by
|
| 19. Based on a preliminary report by a geological survey team, it is estimated that a newly discovered oil field can be expected to produce oil at the rate of
thousand barrels/year, t years after production begins. Find the amount of oil that the field can be expected to yield during the first 17 years of production, assuming that the projection holds true.
|
| 20. Suppose a tractor purchased at a price of $60,000 is to be depreciated by the double declining-balance method over a 10-year period. It can be shown that the rate at which the book value will be decreasing is given by
dollars/year at year t. Find the amount by which the book value of the tractor will depreciate over the first 4 years of its life. Please round the answer to the nearest cent.
|
| 21. A group of marine biologists estimates that if certain conservation measures are implemented, the population of an endangered species of whale will be
where N(t) denotes the population at the end of year t. Find the average population of the whales over the next 2 years.
|
| 22. The manager of TeleStar Cable Service estimates that the total number of subscribers to the service in a certain city t years from now will be
Find the average number of cable television subscribers over the next 4 years if this prediction holds true.
|
| 23. The price of a certain commodity in dollars/unit at time (measured in weeks) is given by
What is the average price of the commodity over the 7-week period from to ? Round the answer to the nearest cent.
|
| 24. Given that and , evaluate:
|
| 25. Given that and , evaluate:
|
| 26. Find the average value of the function
over the indicated interval .
|
| 27. Find the average value of the function
over the indicated interval .
|
| 28. The net investment flow (rate of capital formation) of the giant conglomerate LTF incorporated is projected to be
million dollars/year in year t. Find the accruement on the company’s capital stock in the second year. Hint: The amount is given by Please give your answer to two decimal places. $__________ million
|
| 29. Based on a preliminary report by a geological survey team, it is estimated that a newly discovered oil field can be expected to produce oil at the rate of
thousand barrels/year, t years after production begins. Find the amount of oil that the field can be expected to yield during the first 14 year(s) of production, assuming that the projection holds true. Please round your answer to the nearest whole number. __________ thousand barrels
|
| 30. Suppose a tractor purchased at a price of $60,000 is to be depreciated by the double declining-balance method over a 10-year period. It can be shown that the rate at which the book value will be decreasing is given by
dollars/year at year t. Find the amount by which the book value of the tractor will depreciate over the first 4 years of its life. Please round the answer to the nearest cent. $__________
|
| 31. A group of marine biologists estimates that if certain conservation measures are implemented, the population of an endangered species of whale will be
where N(t) denotes the population at the end of year t. Find the average population of the whales over the next 2 years. Please round your answer to the nearest whole number.
|
| 32. The manager of TeleStar Cable Service estimates that the total number of subscribers to the service in a certain city t years from now will be
Find the average number of cable television subscribers over the next 8 years if this prediction holds true. Please round your answer to the nearest whole number.
|
| 33. The price of a certain commodity in dollars/unit at time t (measured in weeks) is given by
What is the average price of the commodity over the 6-week period from t = 0 to t = 6? Please round the answer to the nearest cent. $__________
|
| 34. Evaluate the given definite integral.
|
| 35. Evaluate the given definite integral.
|
| 36. Evaluate the given definite integral.
|
| 37. Evaluate the given definite integral.
|
| 38. Evaluate the definite integral.
|
| 39. Evaluate the given definite integral.
|
| 40. Evaluate the given definite integral.
|
| 41. Evaluate the given definite integral.
|
| 42. Evaluate the definite integral.
|
| 43. Evaluate the given definite integral.
|
| 44. Evaluate the definite integral.
|
| 45. Evaluate the given definite integral.
|
| 46. Find the average value of the function
over the indicated interval .
|
| 47. Find the average value of the function
over the interval .
|
| 48. A bottle of white wine at room temperature (68°F) is placed in a refrigerator at 5 P.M. Its temperature after t hours is changing at the rate of
°F/hr. By how many degrees will the temperature of the wine have dropped by 11 P.M.? Please round your answer to one decimal place. __________ °F What will the temperature of the wine be at 11 P.M.? Please round your answer to one decimal place. __________ °F
|
| 1. Find the area of the shaded region.
|
| 2. Find the area of the shaded region.
|
| 3. Find the area of the shaded region.
|
| 4. Find the area of the shaded region.
|
| 5. Sketch the graph and find the area of the region bounded below by the graph of the given function and above by the x-axis from to .
|
| 6. Sketch the graph and find the area of the region bounded below by the graph of the given function and above by the x-axis from to .
|
| 7. Find the area of the region bounded below by the graph of the function and above by the x-axis from to .
|
| 8. Sketch the graphs of the functions f and g and find the area of the region enclosed by these graphs and the vertical lines and .
|
| 9. Sketch the graphs of the functions f and g and find the area of the region enclosed by these graphs and the vertical lines and .
|
| 10. Sketch the graphs of the functions f and g and find the area of the region enclosed by these graphs and the vertical lines and .
|
| 11. Find the area of the region enclosed by these graphs and the vertical lines and .
|
| 12. Sketch the graphs of the functions f and g and find the area of the region enclosed by these graphs and the vertical lines and .
|
| 13. Sketch the graph and find the area of the region bounded by the graph of the function f and lines , and .
|
| 14. Sketch the graph and find the area of the region bounded by the graph of the function f and lines , and .
|
| 15. Sketch the graph and find the area of the region bounded by the graph of the function f and lines , and .
|
| 16. Find the area of the region bounded by the graph of the function f and the lines , , and .
|
| 17. Sketch the graph and find the area of the region completely enclosed by the graphs of the given functions f and g.
and
|
| 18. Sketch the region completely enclosed by the graphs of the given functions f and g.
and
|
| 19. Sketch the region completely enclosed by the graphs of the given functions f and g.
and
|
| 20. Find the area of the region completely enclosed by the graphs of the given functions f and g.
|
| 21. In tests conducted by Auto Test Magazine on two identical models of the Phoenix Elite – one equipped with a standard engine and the other with a turbo-charger – it was found that the acceleration of the former is given by
ft/sec, t sec after starting from rest at full throttle, whereas the acceleration of the latter is given by ft/sec. How much faster is the turbo-charged model moving than the model with the standard engine at the end of a 10-second test run at full throttle?
|
| 22. Because of the increasingly important role played by coal as a viable alternative energy source, the production of coal has been growing at the rate of
billion metric tons/year t years from 1970 (which corresponds to ). Had it not been for the energy crisis, the rate of production of coal since 1970 might have been only billion metric tons/year t years from 1970. Determine how much additional coal was produced between 1970 and the end of the century as an alternate energy source. Round your answer to one decimal place.
|
| 23. In an endeavor to curb population growth in a certain country, the government has decided to launch an extensive propaganda campaign. Without curbs, the government expects the rate of population growth to have been
thousand people per year t years from now, over the next 5 years. However, successful implementation of the proposed campaign is expected to result in a population growth rate of thousand people per year t years from now, over the next 5 years. Assuming that the campaign is mounted, how many fewer people will there be in that country 5 years from now then there would have been if no curbs had been imposed? Please round your answer to the nearest integer number of thousands.
|
| 24. Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false.
The area of the region bounded by the graphs of and and the vertical lines and is given by .
|
| 25. Find the area of the shaded region. Round your answer to one decimal place.
|
| 26. Find the area of the shaded region.
|
| 27. In tests conducted by Auto Test Magazine on two identical models of the Phoenix Elite – one equipped with a standard engine and the other with a turbo-charger – it was found that the acceleration of the former is given by
ft/sec, t seconds after starting from rest at full throttle, whereas the acceleration of the latter is given by ft/sec. How much faster is the turbo-charged model moving than the model with the standard engine at the end of a 10-second test run at full throttle? __________ ft/sec
|
| 28. Because of the increasingly important role played by coal as a viable alternative energy source, the production of coal has been growing at the rate of
billion metric tons/year t years from 1960 (which corresponds to ). Had it not been for the energy crisis, the rate of production of coal since 1960 might have been only billion metric tons/year t years from 1960. Determine how much additional coal was produced between 1960 and the end of the century as an alternate energy source. Round your answer to one decimal place. __________ billion metric tons
|
| 29. In an endeavor to curb population growth in a certain country, the government has decided to launch an extensive propaganda campaign. Without curbs, the government expects the rate of population growth to have been
thousand people per year t years from now, over the next 5 years. However, successful implementation of the proposed campaign is expected to result in a population growth rate of thousand people per year t years from now, over the next 5 years. Assuming that the campaign is mounted, how many fewer people will there be in that country 5 years from now then there would have been if no curbs had been imposed? Please round your answer to the nearest whole number. __________ thousand people
|
| 30. Find the area of the shaded region.
|
| 31. Find the area of the shaded region.
|
| 32. Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false.
The area of the region bounded by the graphs of and and the vertical lines and is given by .
|
Original price was: $30.00.$20.00Current price is: $20.00.
Original price was: $30.00.$20.00Current price is: $20.00.
Original price was: $30.00.$20.00Current price is: $20.00.
Original price was: $30.00.$20.00Current price is: $20.00.
Original price was: $30.00.$20.00Current price is: $20.00.
Original price was: $30.00.$20.00Current price is: $20.00.
