Applied Calculus for the Managerial Life and Social Sciences 10e Soo T Tan - Test Bank Instant Download - Complete Test Bank With Answers Sample Questions Are Posted Below 1. Evaluate the expression. a. 81 b. 12 c. 9 d. 8 ANSWER: c POINTS: 1 …
Applied Calculus for the Managerial Life and Social Sciences 10e Soo T Tan - Test Bank Instant Download - Complete Test Bank With Answers Sample Questions Are Posted Below 1. Evaluate the expression. a. 81 b. 12 c. 9 d. 8 ANSWER: c POINTS: 1 …
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Applied Calculus for the Managerial Life and Social Sciences 10e Soo T Tan – Test Bank
Instant Download – Complete Test Bank With Answers
Sample Questions Are Posted Below
| 1. Evaluate the expression.
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| 2. Evaluate the expression.
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| 3. Evaluate the expression.
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| 4. Evaluate the expression.
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| 5. Evaluate the expression.
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| 6. Evaluate the expression.
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| 7. Simplify the expression.
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| 8. Simplify the expression.
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| 9. Simplify the expression.
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| 10. Simplify the expression.
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| 11. Solve the equation for .
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| 12. Solve the equation for .
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| 13. Solve the equation for .
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| 14. Solve the equation for .
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| 15. Solve the equation for .
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| 16. Solve the equation for .
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| 17. Sketch the graphs of the given functions on the same axes.
and
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| 18. Sketch the graphs of the given functions on the same axes.
and
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| 19. Sketch the graphs of the given functions on the same axes.
and
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| 20. Sketch the graphs of the given functions on the same axes.
and
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| 21. Sketch the graphs of the given functions on the same axes.
and
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| 22. Sketch the graphs of the functions on the same axes.
, , and
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| 23. The concentration of a drug in an organ at any time (in seconds) is given by
where is measured in milligrams/cubic centimeter (mg/cm3). What is the concentration to four decimal places of the drug in the organ after 5 sec?
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| 24. The concentration of a drug in an organ at any time t (in seconds) is given by where x(t) is measured in grams/cubic centimeter (g/cm3). Sketch the graph of x.
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| 25. The concentration of a drug in an organ at any time t (in seconds) is given by where x(t) is measured in grams/cubic centimeter (g/cm3).
Select the graph of x.
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| 26. Evaluate the expression.
__________
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| 27. Evaluate the expression.
__________
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| 28. Evaluate the expression.
__________
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| 29. Evaluate the expression.
__________
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| 30. Solve the equation for
. __________
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| 31. Simplify the expression.
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| 32. Simplify the expression.
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| 33. Simplify the expression.
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| 34. Solve the equation for .
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| 35. Solve the equation for .
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| 36. Solve the equation for .
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| 37. Solve the equation for .
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| 38. Solve the equation for .
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| 39. The concentration of a drug in an organ at any time (in seconds) is given by
where is measured in milligrams/cubic centimeter (mg/cm3). What is the initial concentration of the drug in the organ? __________mg/cm3 What is the concentration to four decimal places of the drug in the organ after 10 sec? __________ mg/cm3 What is the concentration to four decimal places of the drug in the organ after 30 sec? __________mg/cm3 What will be the concentration of the drug in the long run? __________mg/cm3
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| 1. Express the equation in logarithmic form.
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| 2. Express the equation in logarithmic form.
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| 3. Express the equation in logarithmic form.
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| 4. Use the facts that and to find the value of the logarithm.
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| 5. Use the facts that to find the value of the logarithm.
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| 6. Use the laws of logarithms to simplify the expression.
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| 7. Write the expression as the logarithm of a single quantity.
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| 8. Use the laws of logarithms to simplify the expression.
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| 9. Use the laws of logarithms to simplify the expression.
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| 10. Sketch the graph of the equation.
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| 11. Use the laws of logarithms to simplify the expression.
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| 12. Sketch the graph of the equation.
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| 13. Use logarithms to solve the equation for t. Round your answer to four decimal places.
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| 14. Use logarithms to solve the equation for t. Round your answer to four decimal places.
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| 15. Use logarithms to solve the equation for t.
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| 16. Use logarithms to solve the equation for t. Please round the answer to four decimal places.
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| 17. On the Richter scale, the magnitude R of an earthquake is given by the formula where I is the intensity of the earthquake being measured and I0 is the standard reference intensity.
Express the intensity I of an earthquake of magnitude in terms of the standard intensity I0. Express the intensity I of an earthquake of magnitude in terms of the standard intensity I0. How many times greater is the intensity of an earthquake of magnitude 8 than one of magnitude 6? In modern times the greatest loss of life attributable to an earthquake occurred in eastern China in 1976. Known as the Tangshan earthquake, it registered 8.2 on the Richter scale. How does the intensity of this earthquake compare with the intensity of an earthquake of magnitude ? Round your answer to the nearest integer.
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| 18. The height (in feet) of a certain kind of tree is approximated by where t is the age of the tree in years. Estimate the age of an 60-ft tree. Round your answer to the nearest hundredth.
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| 19. The height (in feet) of a certain kind of tree is approximated by where t is the age of the tree in years. Estimate the age of an 75-ft tree. Please round the answer to two decimal places.
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| 20. The concentration of a drug in an organ at any time t (in seconds) is given by where is measured in grams/cubic centimeter .
How long would it take for the concentration of the drug in the organ to reach 0.15? How long would it take for the concentration of the drug in the organ to reach 0.12? Round your answer to the nearest hundredth.
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| 21. The concentration of a drug in an organ at any time t (in seconds) is given by where is measured in grams/cubic centimeter . How long would it take for the concentration of the drug in the organ to reach 0.19?
Please round the answer to two decimal places.
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| 22. 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 function is continuous on .
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| 23. Use the definition of a logarithm to prove . Hint: Let and . Then, and .
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| 24. Use the definition of a logarithm to prove .
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| 25. Use the facts that and to find the value of the logarithm. Round your answer to four decimal places.
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| 26. Use the fact that to find the value of the logarithm.
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| 27. Use logarithms to solve the equation for t. Round your answer to four decimal places.
t = __________
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| 28. Use logarithms to solve the equation for t. Round your answer to four decimal places.
t = __________
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| 29. Use logarithms to solve the equation for t. Please round the answer to four decimal places.
t = __________
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| 30. The height (in feet) of a certain kind of tree is approximated by where t is the age of the tree in years. Estimate the age of a 70-ft tree. Round your answer to the nearest hundredth.
__________ years
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| 31. The height (in feet) of a certain kind of tree is approximated by where t is the age of the tree in years. Estimate the age of a 60-ft tree. Please round the answer to two decimal places.
t = __________ years
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| 32. Express the equation in logarithmic form.
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| 33. Express the equation in logarithmic form.
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| 34. Express the equation in logarithmic form.
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| 35. Use the laws of logarithms to simplify the expression.
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| 36. Write the expression as the logarithm of a single quantity.
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| 37. Use the laws of logarithms to simplify the expression.
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| 38. Use the laws of logarithms to simplify the expression.
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| 39. Use the laws of logarithms to simplify the expression.
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| 40. Use logarithms to solve the equation for t.
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| 41. The concentration of a drug in an organ at any time t (in seconds) is given by where is measured in grams/cubic centimeter .
Round your answer to the nearest hundredth. How long would it take for the concentration of the drug in the organ to reach 0.19? __________ seconds How long would it take for the concentration of the drug in the organ to reach 0.12? __________ seconds
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| 42. The concentration of a drug in an organ at any time t (in seconds) is given by where is measured in grams/cubic centimeter .
Please round the answer to two decimal places. How long would it take for the concentration of the drug in the organ to reach 0.17? t = __________ sec How long would it take for the concentration of the drug in the organ to reach 0.15? t = __________ sec
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| 43. 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 function is continuous for all .
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44. Use the definition of a logarithm to prove . Hint: Let and . Then, and .
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45. Use the definition of a logarithm to prove .
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| 1. Find the accumulated amount A if the principal P is invested at an interest rate of r per year for t years. Round your answer to the nearest cent.
P = $2,400, r = 6%, t = 10, compounded semiannually
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| 2. Find the accumulated amount A if the principal P is invested at an interest rate of r per year for t years. Round your answer to the nearest cent.
P = $150,000, r = 7%, t = 3, compounded daily
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| 3. Find the effective rate corresponding to the given nominal rate. Round your answers to two decimal places.
10% / year compounded semiannually _____% 3% / year compounded quarterly _____%
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| 4. Find the effective rate corresponding to the given nominal rate. Round your answers to three decimal places.
6% / year compounded monthly _____% 6% / year compounded daily _____%
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| 5. Find the present value of $20,000 due in 4 year(s) at the given rate of interest. Round your answer to the nearest dollar.
5% / year compounded monthly __________ 8% / year compounded daily __________
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| 6. Find the accumulated amount after 5 year(s) if $7,000 is invested at 9% compounded continuously. Round your answer to the nearest cent.
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| 7. Find the interest rate needed for an investment of $4,000 to grow to an amount of $8,500 in 3 year(s) if interest is compounded monthly. Round your answer to two decimal places.
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| 8. How long will it take $4,000 to grow to $7,500 if the investment earns interest at the rate of 14% / year compounded monthly? Round your answer to one decimal place.
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| 9. How long will it take an investment of $1,000 to double if the investment earns interest at the rate of 8% / year compounded monthly? Round your answer to one decimal place.
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| 10. Find the interest rate needed for an investment of $6,000 to grow to an amount of $7,000 in 3 year(s) if interest is compounded continuously. Round your answer to two decimal places.
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| 11. How long will it take an investment of $5,000 to double if the investment earns interest at the rate of 7% compounded continuously? Round your answer to two decimal places.
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| 12. The Estradas are planning to buy a house 2 year(s) from now. Housing experts in their area have estimated that the cost of a home will increase at a rate of 9% / year during that 2-year period. If this economic prediction holds true, how much can they expect to pay for a house that currently costs $90,000? Round your answer to two decimal places.
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| 13. Bernie invested a sum of money 7 year(s) ago in a savings account, which has since paid interest at the rate of 8% / year compounded quarterly. His investment is now worth $22,927.66. How much did he originally invest? Round your answer to the nearest cent.
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| 14. At an annual inflation rate of 9.5%, how long will it take the Consumer Price Index (CPI) to double? Round your answer to two decimal places.
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| 15. Online retail sales stood at $22.7 billion for 2000. For the next 2 years, they grew by 32.4% and 27.6% per year, respectively. For the next 6 years, online retail sales are projected to grow at 30.2%, 19.7%, 24.3%, 13.6%, 17.2%, and 10.6% per year, respectively. What are the projected online sales for 2008? Round your answer to one decimal place.
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| 16. Julio purchased 700 shares of a certain stock for $22,750 (including commissions). He sold the shares 5 year(s) later and received $32,100 after deducting commissions. Find the effective annual rate of return on his investment over the 5-year period. Round your answer to two decimal places.
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| 17. Find the present value of $54,049 due in 5 year(s) at an interest rate of 7% / year compounded continuously. Round your answer to the nearest integer.
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| 18. A condominium complex was purchased by a group of private investors for $1.2 million and sold 5 year(s) later for $3.7 million. Find the annual rate of return (compounded continuously) on their investment. Round your answer to two decimal places.
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| 19. Having received a large inheritance, a child’s parents wish to establish a trust for the child’s college education. If 7 year(s) from now they need an estimated $60,000, how much should they set aside in trust now, if they invest the money at the given rate of interest. Round your answer to the nearest cent.
13.5% compounded quarterly _________ 13.5% compounded continuously _________
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| 20. A condominium complex was purchased by a group of private investors for $1.3 million and sold 7 year(s) later for $3.9 million. Find the annual rate of return (compounded continuously) on their investment. Round your answer to two decimal places.
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| 21. Eleni, who is now 55 years old, is employed by a firm that guarantees her a pension of $90,000/year at age 70. What is the present value of her first year’s pension if inflation over the next 15 year(s) is at the given rate. Assume that inflation is continuously compounded. Round your answer to the nearest cent.
6% _________ 9% _________ 18% _________
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| 22. An investor purchased a piece of waterfront property. Because of the development of a marina in the vicinity, the market value of the property is expected to increase according to the rule where V(t) is measured in dollars and t is the time in years from the present. If the inflation rate is expected to be 10% compounded continuously for the next 8 years, what is P(t) expected to be in 4 years? Round your answer to the nearest dollar.
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| 23. Find the nominal interest rate that, when compounded monthly, yields an effective interest rate of 16% / year. Round your answer to two decimal places.
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| 24. Find the nominal interest rate that, when compounded continuously, yields an effective interest rate of 10% / year. Round your answer to three decimal places.
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| 25. Find the accumulated amount A if the principal P is invested at an interest rate of r per year for t years. Round your answer to the nearest cent.
P = $2,400, r = 9%, t = 10, compounded semiannually $__________
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| 26. Find the accumulated amount A if the principal P is invested at an interest rate of r per year for t years. Round your answer to the nearest cent.
P = $180,000, r = 6%, t = 3, compounded daily $__________
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| 27. Find the accumulated amount after 6 year(s) if $5,000 is invested at 8% compounded continuously. Round your answer to the nearest cent.
$__________
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| 28. Find the interest rate needed for an investment of $3,000 to grow to an amount of $8,500 in 3 year(s) if interest is compounded monthly. Round your answer to the nearest hundredth.
__________%
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| 29. How long will it take $3,000 to grow to $8,500 if the investment earns interest at the rate of 18% / year compounded monthly? Round your answer to the nearest tenth.
__________ year(s)
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| 30. How long will it take an investment of $8,000 to double if the investment earns interest at the rate of 8% / year compounded monthly? Round your answer to the nearest tenth.
__________ year(s)
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| 31. Find the interest rate needed for an investment of $6,000 to grow to an amount of $8,000 in 3 year(s) if interest is compounded continuously. Round your answer to the nearest hundredth.
Interest rate is __________% per year.
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| 32. How long will it take an investment of $4,000 to double if the investment earns interest at the rate of 7% compounded continuously? Round your answer to the nearest hundredth.
__________ year(s)
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| 33. The Estradas are planning to buy a house 4 year(s) from now. Housing experts in their area have estimated that the cost of a home will increase at a rate of 8% / year during that 4-year period. If this economic prediction holds true, how much can they expect to pay for a house that currently costs $40,000? Round your answer to the nearest cent.
$__________
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| 34. Bernie invested a sum of money 5 year(s) ago in a savings account, which has since paid interest at the rate of 6% / year compounded quarterly. His investment is now worth $22,927.66. How much did he originally invest? Round your answer to the nearest cent.
$__________
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| 35. At an annual inflation rate of 5.5%, how long will it take the Consumer Price Index (CPI) to double? Round your answer to the nearest hundredth.
__________ year(s)
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| 36. Online retail sales stood at $23.5 billion for 2000. For the next 2 years, they grew by 32.8% and 27.7% per year, respectively. For the next 6 years, online retail sales are projected to grow at 30.5%, 19.3%, 24.4%, 13.8%, 17.8%, and 10.3% per year, respectively. What are the projected online sales for 2008? Round your answer to the nearest tenth.
$__________ billion
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| 37. Julio purchased 400 shares of a certain stock for $24,750 (including commissions). He sold the shares 6 year(s) later and received $32,800 after deducting commissions. Find the effective annual rate of return on his investment over the 6-year period. Round your answer to the nearest hundredth.
__________%
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| 38. Find the present value of $59,835 due in 3 year(s) at an interest rate of 9% / year compounded continuously. Round your answer to the nearest dollar.
$__________
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| 39. A condominium complex was purchased by a group of private investors for $1.4 million and sold 4 year(s) later for $3.1 million. Find the annual rate of return (compounded continuously) on their investment. Round your answer to the nearest hundredth.
__________%
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| 40. A condominium complex was purchased by a group of private investors for $1.3 million and sold 6 year(s) later for $3.8 million. Find the annual rate of return (compounded continuously) on their investment. Round your answer to the nearest hundredth.
Annual rate is __________% per year.
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| 41. Find the nominal interest rate that, when compounded monthly, yields an effective interest rate of 20% / year. Round your answer to the nearest hundredth.
__________%
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| 42. Find the nominal interest rate that, when compounded continuously, yields an effective interest rate of 8% / year. Round your answer to the nearest thousandth.
__________%
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| 43. Find the effective rate corresponding to the given nominal rate. Round your answers to the nearest hundredth.
10% / year compounded semiannually __________% 3% / year compounded quarterly __________%
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| 44. Find the effective rate corresponding to the given nominal rate. Round your answers to the nearest thousandth.
5% / year compounded monthly __________ % 5% / year compounded daily __________ %
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| 45. Find the present value of $70,000 due in 4 year(s) at the given rate of interest. Round your answers to the nearest dollar.
4% / year compounded monthly $__________ 9% / year compounded daily $__________
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| 46. Having received a large inheritance, a child’s parents wish to establish a trust for the child’s college education. If 7 year(s) from now they need an estimated $60,000, how much should they set aside in trust now, if they invest the money at the given rate of interest. Round your answer to the nearest cent.
13.5 compounded quarterly $__________ 13.5 compounded continuously $__________
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| 47. Eleni, who is now 50 years old, is employed by a firm that guarantees her a pension of $40,000/year at age 65. What is the present value of her first year’s pension if inflation over the next 15 year(s) is at the given rate. Assume that inflation is continuously compounded. Round your answers to the nearest cent.
6% $__________ 7% $__________ 18% $__________
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| 1. Find the derivative of the function.
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| 2. Find the derivative of the function.
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| 3. Find the derivative of the function.
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| 4. Find the derivative of the function.
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| 5. Find the derivative of the function.
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| 6. Find the derivative of the function.
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| 7. Find the derivative of the function.
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| 8. Find the derivative of the function.
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| 9. Find the derivative of the function.
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| 10. Find the derivative of the function.
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| 11. Find the second derivative of the function.
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| 12. Find the second derivative of the function.
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| 13. Determine the intervals where the function is decreasing.
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| 14. Determine the intervals of concavity for the function.
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| 15. Use the curve-sketching guideline, to select the graph of the function.
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| 16. Use the curve-sketching guideline, to sketch the graph of the function.
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| 17. Based on data obtained from the Census Bureau, the manager of Plymouth Van Lines estimates that the percent of the total population relocating in year t ( corresponds to the year 1960) may be approximated by the formula .
Compute P‘(10), P'(20), and P'(30).
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| 18. A women’s clothing chain store, found that t days after the end of a sales promotion the volume of sales was given by dollars. Find to the nearest integer the rate of change of sales volume when t = 1.
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| 19. The unit selling price p (in dollars) and the quantity demanded (in pairs) of a certain brand of women’s gloves is given by the demand equation .
What is the marginal revenue to the nearest cent per day when x = 100?
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| 20. The monthly demand for a certain brand of perfume is given by the demand equation where p denotes the retail unit price (in dollars) and x denotes the quantity (in 1-oz bottles) demanded. Find the rate of change of the price to the nearest hundredth of a cent per bottle when x = 1,000.
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| 21. The monthly demand for a certain brand of table wine is given by the demand equation
where p denotes the wholesale price per case (in dollars) and x denotes the number of cases demanded. Find the rate of change of the price to the nearest hundredth of a cent per case when x = 1,000.
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| 22. The Ehrenberg equation gives the relationship between the height (in meters) and the average weight W (in kilograms) for children between 5 and 13 years of age.
What is the average weight of a 10-year-old child who stands at 1.4 m tall? Round the answer to the nearest tenth. Use differentials to estimate the change in the average weight of a 10-year-old child whose height increases from 1.4 m to 1.45 m.
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| 23. The price of a certain commodity in dollars per unit at time t (measured in weeks) is given by
. Find the equilibrium price of the commodity. (Hint: It’s given by . Also, use the fact that .)
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| 24. A study on worldwide oil use was prepared for a major oil company. The study predicted that the amount of oil used to fuel productivity in a certain country is given by
where f (t) denotes the number of barrels per $1,000 of economic output and t is measured in decades ( corresponds to 1965). Compute f ‘(0) and f '(2). Round the answer to the nearest hundredth.
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| 25. The price of a certain commodity in dollars per unit at time t (measured in weeks) is given by
. How fast is the price of the commodity changing at ?
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| 26. A women’s clothing chain store, found that t days after the end of a sales promotion the volume of sales was given by dollars. Find to the nearest dollar the rate of change of sales volume when t = 2.
$__________
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| 27. Find the derivative of the function.
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| 28. Find the derivative of the function.
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| 29. Find the derivative of the function.
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| 30. Find the derivative of the function.
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| 31. Find the derivative of the function.
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| 32. Find the derivative of the function.
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| 33. Find the derivative of the function.
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| 34. Find the derivative of the function.
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| 35. Find the derivative of the function.
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| 36. Find the derivative of the function.
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| 37. Find the second derivative of the function.
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| 38. Find the second derivative of the function.
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| 39. The monthly demand for a certain brand of perfume is given by the demand equation
where p denotes the retail unit price (in dollars) and x denotes the quantity (in 1-oz bottles) demanded. Find the rate of change of the price to the nearest hundredth of a cent per bottle when x = 2,000. __________ cents per bottle What is the price per bottle when x = 2,000. $__________ / bottle
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| 40. The monthly demand for a certain brand of table wine is given by the demand equation
where p denotes the wholesale price per case (in dollars) and x denotes the number of cases demanded. Find the rate of change of the price to the nearest hundredth of a cent per case when x = 1,000. __________ cents per case What is the price per case when x = 1,000. $__________ / case
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| 41. The Ehrenberg equation gives the relationship between the height (in meters) and the average weight W (in kilograms) for children between 5 and 13 years of age.
Round your answer to the nearest tenth. What is the average weight of a 10-year-old child who stands at 1.4 m tall? ________ kg Use differentials to estimate the change in the average weight of a 10-year-old child whose height increases from 1.4 m to 1.45 m. ________ kg
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| 42. The price of a certain commodity in dollars per unit at time t (measured in weeks) is given by
. What is the price of the commodity at t = 0? $__________ / unit How fast is the price of the commodity decreasing at t = 0? $__________ / wk Find the equilibrium price of the commodity. (Hint: It’s given by . Also, use the fact that .) $__________ / unit
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| 43. The price of a certain commodity in dollars per unit at time t (measured in weeks) is given by
. What is the price of the commodity at ? $__________/unit How fast is the price of the commodity changing at ? __________ (increasing / decreasing) at the rate of $__________/wk Find the equilibrium price of the commodity. (Hint: It’s given by . Also, use the fact that .) $__________/unit
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| 1. Find the derivative of the function.
|
| 2. Find the derivative of the function.
|
| 3. Find the derivative of the function.
|
| 4. Find the derivative of the function.
|
| 5. Find the derivative of the function.
|
| 6. Find the derivative of the function.
|
| 7. Find the derivative of the function.
|
| 8. Find the derivative of the function.
|
| 9. Find the derivative of the function.
|
| 10. Find the derivative of the function.
|
| 11. Find the derivative of the function.
|
| 12. Find the derivative of the function.
|
| 13. Find the second derivative of the function.
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| 14. Find the second derivative of the function.
|
| 15. Use logarithmic differentiation to find the derivative of the function.
|
| 16. Use logarithmic differentiation to find the derivative of the function.
|
| 17. Use logarithmic differentiation to find the derivative of the function.
|
| 18. Find an equation of the tangent line to the graph of at the point .
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| 19. Find the inflection points of the function .
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| 20. Find an equation of the tangent line to the graph of at its inflection point.
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| 21. The strain (percent of compression) on the lumbar vertebral disks in an adult human as a function of the load x (in kilograms) is given by .
What is the rate of change of the strain with respect to the load when the load is 50 kg? When the load is 300 kg? Give the answers to four decimal places.
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| 22. For children between the ages of 5 and 13 years old, the Ehrenberg equation gives the relationship between the weight W (in kilograms) and the height h (in meters) of a child. Use differentials to estimate the change in the weight of a child who grows from 1 m to 1.2 m.
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| 23. Use the curve-sketching guideline, to select the graph of the function.
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| 24. On the Richter scale, the magnitude R of an earthquake is given by the formula where I is the intensity of the earthquake being measured and I0 is the standard reference intensity. Suppose an earthquake is measured with a magnitude of 5 on the Richter scale with an error of at most 2%. Use differentials to find the error in the intensity of the earthquake. Round your answer to the nearest integer.
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| 25. For children between the ages of 5 and 13 years old, the Ehrenberg equation gives the relationship between the weight W (in kilograms) and the height h (in meters) of a child. Use differentials to estimate the change in the weight of a child who grows from 1.1 m to 1.3 m. Round the answer to the nearest tenth.
__________ kg
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| 26. Find the derivative of the function.
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| 27. Find the derivative of the function.
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| 28. Find the derivative of the function.
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| 29. Find the derivative of the function.
|
| 30. Find the derivative of the function.
|
| 31. Find the derivative of the function.
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| 32. Find the derivative of the function.
|
| 33. Find the derivative of the function.
|
| 34. Find the derivative of the function.
|
| 35. Find the derivative of the function.
|
| 36. Find the derivative of the function.
|
| 37. Find the derivative of the function.
|
| 38. Find the second derivative of the function.
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| 39. Find the second derivative of the function.
|
| 40. Use logarithmic differentiation to find the derivative of the function.
|
| 41. Use logarithmic differentiation to find the derivative of the function.
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| 42. Use logarithmic differentiation to find the derivative of the function.
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43. Find an equation of the tangent line to the graph of at the point .
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44. Find the inflection points of the function .
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| 45. The strain (percent of compression) on the lumbar vertebral disks in an adult human as a function of the load x (in kilograms) is given by .
Give the answer to four decimal places. What is the rate of change of the strain with respect to the load when the load is 100 kg? __________ What is the rate of change of the strain with respect to the load when the load is 350 kg? __________
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| 46. On the Richter scale, the magnitude R of an earthquake is given by the formula where I is the intensity of the earthquake being measured and I0 is the standard reference intensity.
What is the magnitude of an earthquake that has intensity 10 millions times that of I0? R = __________ Suppose an earthquake is measured with a magnitude of 5 on the Richter scale with an error of at most 2%. Use differentials to find the error in the intensity of the earthquake. Hint: Observe that and use logarithmic differentiation. Round your answer to the nearest integer. __________I0
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47. Find an equation of the tangent line to the graph of at its inflection point.
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1. Given that a quantity Q(t) is described by the exponential growth function where t is measured in minutes. What is the growth constant? What quantity is present initially? Complete the table of values. Round your answers to the nearest integer.
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| 2. Given that a quantity Q(t) exhibiting exponential decay is described by the function where t is measured in years. What is the decay constant? What quantity is present initially? Complete the table of values. Round your answer to the nearest integer.
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| 3. The growth rate of the bacterium, a common bacterium found in the human intestine, is proportional to its size. Under ideal laboratory conditions, when this bacterium is grown in a nutrient broth medium, the number of cells in a culture doubles approximately every 20 min. If the initial cell population is 10, determine the function Q(t) that expresses the exponential growth of the number of cells of this bacterium as a function of time t (in minutes). How long will it take for a colony of 10 cells to increase to a population of 1 million? If the initial cell population were 100, how would this alter the model?
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| 4. A certain piece of machinery was purchased 2 year(s) ago by Garland Mills for $500,000. Its present resale value is $320,000. Assuming that the machine’s resale value decreases exponentially, what will it be 2 year(s) from now?
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| 5. If the temperature is constant, then the atmospheric pressure P (in pounds/square inch) varies with the altitude above sea level h in accordance with the law where p0 is the atmospheric pressure at sea level and k is a constant.
If the atmospheric pressure is 17 lb/in.2 at sea level and 11.5 lb/in.2 at 5,000 ft, how fast is the atmospheric pressure changing with respect to altitude at an altitude of 15,000 ft? Give the answer to four decimal places.
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| 6. The radioactive element polonium decays according to the law where Q0 is the initial amount and the time t is measured in days. If the amount of polonium left after 560 days is 40 mg, what was the initial amount present?
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| 7. Phosphorus 32 has a half-life of 14.2 days. If 600 g of this substance are present initially, find the amount present after t days. What amount will be left after 3.55 days? How fast is the phosphorus 32 decaying when t = 3.55?
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| 8. Strontium 90, a radioactive isotope of strontium, is present in the fallout resulting from nuclear explosions. It is especially hazardous to animal life, including humans, because, upon ingestion of contaminated food, it is absorbed into the bone structure. Its half-life is 27 years. If the amount of strontium 90 in a certain area is found to be eight times the “safe” level, find how much time must elapse before an “acceptable level” is reached.
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| 9. Wood deposits recovered from an archeological site contain 24% of the carbon 14 they originally contained. How long ago did the tree from which the wood was obtained die? Hint: the decay constant k for carbon 14 is equal to 0.00012.
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| 10. Skeletal remains of the so-called “Pittsburgh Man”, unearthed in Pennsylvania, had lost 74% of the carbon 14 they originally contained. Determine the approximate age of the bones. Hint: the decay constant k for carbon 14 is equal to 0.00012.
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| 11. The American Court Reporting Institute finds that the average student taking Advanced Machine Shorthand, an intensive 20-week course, progresses according to the function , where Q(t) measures the number of words (per minute) of dictation that the student can take in machine shorthand after t weeks in the course. Sketch the graph of the function Q and answer the following questions:
a.What is the beginning shorthand speed for the average student in this course? b.What shorthand speed does the average student attain halfway through the course? c.How many words per minute can the average student take after completing this course?
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| 12. Universal Instruments found that the monthly demand for its new line of Galaxy Home Computers t months after placing the line on the market was given by .
Select the graph of this function. At what level is the demand expected to stabilize?
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| 13. The percent of a certain brand of computer chips that will fail after t years of use is estimated to be
. What percent of this brand of computer chips are expected to be usable after 6 years?
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| 14. The length (in centimeters) of a typical Pacific halibut t years old is approximately
. What is the length of a typical 5-year-old Pacific halibut? How fast is the length of a typical 5-year-old Pacific halibut increasing? What is the maximum length a typical Pacific halibut can attain?
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| 15. During a flu epidemic, the number of children in the Woodbridge Community School System who contracted influenza after t days was given by .
How many children were stricken by the flu after the first day? How many children had the flu after 10 days? How many children eventually contracted the disease?
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| 16. The change from religious to lay teachers at Roman Catholic schools has been partly attributed to the decline in the number of women and men entering religious orders. The percent of teachers who are lay teachers is given by where t is measured in decades, with corresponding to the beginning of 1960.
Find the year when the percent of lay teachers was increasing most rapidly.
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| 17. On the basis of data collected during an experiment, a biologist found that the growth of the fruit fly (Drosophila) with a limited food supply could be approximated by the exponential model where t denotes the number of days since the beginning of the experiment.
How fast was the population changing on the 20th day?
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| 18. According to estimates by Paul Kroger Associates, the percent of households that own VCRs is given by where t is measured in years, with t = 0 corresponding to the beginning of 1985. What percent of households owned VCRs at the beginning of 1985? At the beginning of 1990?
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| 19. The U.S. population is approximated by the function where P(t) is measured in millions of people and t is measured in 30-year intervals, with t = 0 corresponding to 1930. What is the expected population of the United States in 2020 ( t = 3 )?
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| 20. Three hundred students attended the dedication ceremony of a new building on a college campus. The president of the traditionally female college announced a new expansion program, which included plans to make the college coeducational. The number of students who learned of the new program t hours later is given by the function .
If 600 students on campus had heard about the new program 2 hours after the ceremony, how many students had heard about the policy after 4 hours?
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| 21. The length (in centimeters) of a common commercial fish is approximated by the von-Bertalanffy growth function where a, b, and k are positive constants.
Select the graph of f.
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| 22. The concentration of a drug in grams/cubic centimeter (g/cm3) t minutes after it has been injected into the bloodstream is given by where w, p, and k are positive constants, with p > w.
At what time is the concentration of the drug the greatest? What will be the concentration of the drug in the long run?
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| 23. Suppose a radioactive substance decays according to the formula . How long will it take for the substance to decay to half the original amount?
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| 24. A certain piece of machinery was purchased 5 years ago by Garland Mills for $400,000. Its present resale value is $256,000. Assuming that the machine’s resale value decreases exponentially, what will it be 2 years from now? Round your answer to the nearest dollar.
$__________
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| 25. The radioactive element polonium decays according to the law , where Q0 is the initial amount and the time t is measured in days. If the amount of polonium left after 280 days is 80 mg, what was the initial amount present?
__________ mg
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| 26. Strontium 90, a radioactive isotope of strontium, is present in the fallout resulting from nuclear explosions. It is especially hazardous to animal life, including humans, because, upon ingestion of contaminated food, it is absorbed into the bone structure. Its half-life is 27 years. If the amount of strontium 90 in a certain area is found to be eight times the “safe” level, find how much time must elapse before an “acceptable level” is reached.
__________ years
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| 27. Wood deposits recovered from an archeological site contain 28% of the carbon 14 they originally contained. How long ago did the tree from which the wood was obtained die? Round your answer to the nearest year. Hint: the decay constant k for carbon 14 is equal to 0.00012.
__________ years
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| 28. Skeletal remains of the so-called “Pittsburgh Man”, unearthed in Pennsylvania, had lost 74% of the carbon 14 they originally contained. Determine the approximate age of the bones. Round your answer to the nearest year. Hint: the decay constant k for carbon 14 is equal to 0.00012.
__________ years
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| 29. The percent of a certain brand of computer chips that will fail after t years of use is estimated to be .
What percent of this brand of computer chips are expected to be usable after 6 years? Round your answer to one decimal place. __________%
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| 30. The U.S. population is approximated by the function , where P(t) is measured in millions of people and t is measured in 30-year intervals, with t = 0 corresponding to 1930. What is the expected population of the United States in 2020 (t = 3)? Round your answer to one decimal place.
__________ million
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| 31. If the temperature is constant, then the atmospheric pressure P (in pounds/square inch) varies with the altitude above sea level h in accordance with the law , where p0 is the atmospheric pressure at sea level and k is a constant.
If the atmospheric pressure is 17 lb/in.2 at sea level and 12.5 lb/in.2 at 6,000 ft, find the atmospheric pressure at an altitude of 18,000 ft. Please round the answer to one decimal place. __________ lb/in.2 How fast is the atmospheric pressure changing with respect to altitude at an altitude of 18,000 ft? Please round the answer to four decimal places. __________ lb/in.2/ft
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32. The length (in centimeters) of a typical Pacific halibut t years old is approximately . What is the length of a typical 6-year-old Pacific halibut? How fast is the length of a typical 6-year-old Pacific halibut increasing? What is the maximum length a typical Pacific halibut can attain? Round your answers to the nearest tenth.
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| 33. During a flu epidemic, the number of children in the Woodbridge Community School System who contracted influenza after t days was given by .
How many children were stricken by the flu after the first day? Round your answer to the nearest integer. __________ children How many children had the flu after 10 days? Round your answer to the nearest integer. __________ children How many children eventually contracted the disease? Round your answer to the nearest integer. __________ children
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| 34. The change from religious to lay teachers at Roman Catholic schools has been partly attributed to the decline in the number of women and men entering religious orders. The percent of teachers who are lay teachers is given by where t measured in decades, with t = 0 corresponding to the beginning of 1960.
What percent of teachers were lay teachers at the beginning of 1990? Please round the answer to one decimal place. __________ % How fast was the percent of lay teachers changing at the beginning of 1990? Please round the answer to two decimal places. __________ % / year Find the year when the percent of lay teachers was increasing most rapidly.
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| 35. On the basis of data collected during an experiment, a biologist found that the growth of the fruit fly (Drosophila) with a limited food supply could be approximated by the exponential model , where t denotes the number of days since the beginning of the experiment.
What was the initial fruit fly population in the experiment? __________ What was the maximum fruit fly population that could be expected under this laboratory condition? __________ What was the population of the fruit fly colony on the 20th day? Please give the answer as an integer. __________ How fast was the population changing on the 20th day? Please give the answer as an integer. __________
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| 36. According to estimates by Paul Kroger Associates, the percent of households that own VCRs is given by , where t is measured in years, with t = 0 corresponding to the beginning of 1985.
What percent of households owned VCRs at the beginning of 1985? Round your answer to the nearest tenth. __________% At the beginning of 1992? Round your answer to the nearest tenth. __________%
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| 37. Three hundred students attended the dedication ceremony of a new building on a college campus. The president of the traditionally female college announced a new expansion program, which included plans to make the college coeducational. The number of students who learned of the new program t hours later is given by the function .
If 600 students on campus had heard about the new program 2 hours after the ceremony, how many students had heard about the policy after 4 hours? __________ How fast was the news spreading 4 hours after the ceremony? Round the answer to the nearest integer. __________
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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.