College Algebra 12e R David Gustafson Jeff Hughes - Test Bank Instant Download - Complete Test Bank With Answers Sample Questions Are Posted Below 1. Use a calculator to find the value to four decimal places. a. 136.0665 b. 125.0000 c. 4.0249 d. 20.1246 e. …
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College Algebra 12e R David Gustafson Jeff Hughes – Test Bank
Instant Download – Complete Test Bank With Answers
Sample Questions Are Posted Below
| 1. Use a calculator to find the value to four decimal places.
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| 2. Simplify the expression.
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| 3. Simplify the expression. Round your answer to two decimal places, if necessary.
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| 4. Graph the function.
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| 5. Find the value of b that would cause the graph of y = bx to look like the graph indicated.
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| 6. Find the value of b that would cause the graph of y = bx to look like the graph indicated.
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| 7. Find the value of b that would cause the graph of y = bx to look like the graph below.
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| 8. Graph the exponential function.
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| 9. Graph the function using translations.
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| 10. Graph the function using translations.
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| 11. Graph the function using translations.
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| 12. Graph the function using translations.
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| 13. An initial deposit of $800 earns 4% interest, compounded quarterly. How much will be in the account in 7 years? Round to the nearest cent.
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| 14. How much more interest could $300 earn in 10 years, compounded semiannually (two times a year), if the annual interest rate were 7% instead of 6%?
Assume that there are no deposits or withdrawals and round to the nearest cent.
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| 15. Some financial institutions pay daily interest, compounded by the 360/365 method, using the formula
(t is in years). Using this method, what will an initial investment of $1,800 be worth in 9 years, assuming a 9% annual interest rate? Round to the nearest cent.
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| 16. A bank credit card charges interest at the rate of 13% per year, compounded monthly. If a senior in college charges her last tuition bill of $1,100 and intends to pay it in one year, what will she have to pay? Round to the nearest cent.
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| 17. An initial investment of $1,300 earns 19% interest, compounded continuously. What will the investment be worth in 10 years? Round to the nearest cent.
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| 18. An account now contains $8,800 and has been accumulating interest at a 16% annual rate, compounded continuously, for 7 years. Find the initial deposit and round to the nearest cent.
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| 19. If $10,000 is invested at an interest rate of 6% per year, compounded semiannually, find the value of the investment after 15 years. Round to the nearest cent.
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| 20. If $6,000 is invested at an interest rate of 6% per year, compounded monthly, find the amount of the investment at the end of 2 years. Round to the nearest cent.
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| 21. The present value of a sum of money is the amount that must be invested now, at a given rate of interest, to produce the desired sum at a later date. Find the present value of $1,000 if interest is paid at a rate of 9% per year, compounded semiannually, for 2 years. Round to the nearest cent.
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| 22. Find the values of a and b that would cause the graph of to pass through the points and .
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| 23. Select the graphs that could represent an exponential function of the form:
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| 24. An account now contains $11,200.00 and has been accumulating interest at a 17% annual rate, compounded continuously, for 4 years. Find the initial deposit, rounded to the nearest cent.
$ __________
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| 25. Use a calculator to find the value to four decimal places.
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| 26. Simplify the expression.
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| 27. Find the value of b that would cause the graph of y = bx to look like the graph below.
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| 28. Find the value of b, if any, that would cause the graph of y = bx to look like the graph below.
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| 29. An initial deposit of $500 earns 5% interest, compounded quarterly. How much will be in the account in 14 years?
Please enter your answer as a number without the units, rounded to the nearest hundredth.
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| 30. How much more interest could $200 earn in 10 years, compounded semiannually (two times a year), if the annual interest rate were 10% instead of 2%?
Assume that there are no deposits or withdrawals. Please enter your answer as a number without the units, rounded to the nearest hundredth.
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| 31. Some financial institutions pay daily interest, compounded by the 360/365 method, using the formula
(t is in years). Using this method, what will an initial investment of $1,500 be worth in 6 years, assuming a 8% annual interest rate? Please enter your answer as a number without the units, rounded to the nearest hundredth.
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| 32. A bank credit card charges interest at the rate of 13% per year, compounded monthly. If a senior in college charges her last tuition bill of $1,800 and intends to pay it in one year, what will she have to pay?
Please enter your answer as a number without the units, rounded to the nearest hundredth.
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| 33. An initial investment of $1,600 earns 27% interest, compounded continuously. What will the investment be worth in 11 years?
Please enter your answer as a number without the units, rounded to the nearest hundredth.
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| 34. If $100,000 is invested at an interest rate of 10% per year, compounded semiannually, find the value of the investment after 10 years.
Please enter your answer as a number without the units, rounded to the nearest hundredth.
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| 35. The present value of a sum of money is the amount that must be invested now, at a given rate of interest, to produce the desired sum at a later date. Find the present value of $100,000 if interest is paid at a rate of 6% per year, compounded semiannually, for 7 years.
Please enter your answer as a number without the units, rounded to the nearest hundredth.
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| 36. Simplify the expression.
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| 37. Find the value of b that would cause the graph of y = bx to look like the graph below.
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| Match each graph with its corresponding function.
Choose the correct letter for each question.
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38.
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39.
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40.
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| Tell whether each graph in the left column could represent an exponential function of the form .
Choose the correct letter for each question.
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41.
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42.
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43.
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| 44. If an investment is growing continuously for t years, its annual growth rate r is given by the
formula where P is the current value and Po is the amount originally invested. An investment of $13,500 in a particular Internet company in 1992 was worth $13,500,000 in 2000. Find this investment’s average annual growth rate during this period.
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| 1. Tritium, a radioactive isotope of hydrogen, has a half-life of 12.4 years. Of an initial sample of 41 grams, how much will remain after 94 years? Round your answer to four decimal places.
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| 2. In April of 1986, the world’s worst nuclear power disaster occurred at Chernobyl in the former USSR. An explosion released about 924 kilograms of radioactive cesium-137 (137 Cs) into the atmosphere. If the half-life of 137 Cs is 30.17 years, how much will remain in the atmosphere in 148 years? Round your answer to four decimal places.
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| 3. One isotope of holmium, 162 Ho, has a half-life of 22 minutes. The half-life of a second isotope, 164 Ho, is 37 minutes. Starting with a sample containing equal amounts, find the ratio of the amounts of 162 Ho to 164 Ho after 42 minutes.
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| 4. The biological half-life of the asthma medication theophylline is 4.5 hours for smokers. Find the amount of the drug retained in a smoker’s system 12 hours after a dose of 1 unit is taken. Round your answer to three decimal places.
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| 5. A Wisconsin lake is stocked with 10,000 bluegill. The population is expected to grow exponentially according to the model . How many bluegill will be in the lake in 10 years?
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| 6. The intensity I of light (in lumens) at a distance x meters below the surface is given by I = Iok x , where Io is the intensity at the surface and k depends on the clarity of the water. At one location in the Arctic Ocean, Io = 9 and k = 0.7. Find the intensity at a depth of 6 meters. Round your answer to two decimal places.
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| 7. A colony of 5 million bacteria is growing in a culture medium. The population P after t hours is given by the formula. Find the population after 6 hours. Round to the nearest million.
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| 8. The growth of a town’s population is modeled by . How large will the population be when ? Round to a whole number.
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| 9. In one individual, the percent alcohol level t minutes after two shots of whiskey is given by . Find the blood alcohol level after 13 minutes. Round to the nearest thousandths.
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| 10. The population of the Earth is approximately 6 billion people and is growing at an annual rate of 1.2%. Assuming a Malthusian growth model, find the world population in 20 years. Round your answer to the nearest hundredths.
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| 11. The population of the Earth is approximately 7 billion people and is growing at an annual rate of 2%. Assuming a Malthusian growth model, by what factor will the current population of the Earth increase in 50 years? Round to the nearest hundredths.
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| 12. The percent P of the drug triazolam (a drug for treating insomnia) remaining in a person’s bloodstream after t hours is given by . What percent will remain in the bloodstream after 12 hours? Round to the nearest hundredths.
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| 13. The concentration x of a certain drug in an organ after t minutes is given by . Find the concentration of the drug at 20 minutes. Round your answer to four decimal places.
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| 14. The concentration x of a certain drug in an organ after t minutes is given by . Find the initial concentration of the drug when .
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| 15. In a city with a population of 1,200,000, there are currently 1,000 cases of infection with the HIV virus. If the spread of the disease is projected by the formula
how many people will be infected in 9 years? Round your answer to the nearest hundreds.
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| 16. The life expectancy of white females can be estimated by using the function , where x is the current age. Find the life expectancy of a white female who is currently 37 years old. Round to one decimal place.
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| 17. The width w (in millimeters) of successive growth spirals of the sea shell Catapulus voluto, shown in the illustration, is given by the function , where n is the spiral number. To the nearest tenth of a millimeter, find the width of the second spiral.
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| 18. Before the parachute opens, the velocity v (in meters per second) of a skydiver is given by , where t is time in seconds into the jump. Find the velocity after 18 seconds. Round to two decimal places.
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| 19. Before the parachute opens, the velocity v (in meters per second) of a skydiver is given by , where t is time in seconds into the jump. After t seconds, a certain falling object has a velocity v given by . What is the difference in their velocities after 27 seconds? Round to two decimal places.
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| 20. In 1999, the male population of the United States was about 133 million, and the female population was about 139 million. Assuming a Malthusian growth model with a 1.4% annual growth rate, how many more females than males will there be in 26 years? Round your answer to the nearest tenths.
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| 21. Some hot water, initially at C, is placed in a room with a temperature of C. The temperature T of the water after t hours is given by . Find the temperature in 2.3 hours. Round your answer to the nearest hundredths.
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| 22. One isotope of holmium, 162 Ho, has a half-life of 22 minutes. The half-life of a second isotope, 164 Ho, is 37 minutes. Starting with a sample containing equal amounts, find the ratio of the amounts of 162 Ho to 164 Ho after 32 minutes.
Please give the answer to four decimal places.
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| 23. Tritium, a radioactive isotope of hydrogen, has a half-life of 12.4 years. Of an initial sample of 13 grams, how much will remain after 98 years?
Please enter your answer as a number without the units, rounded to four decimal places.
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| 24. In April of 1986, the world’s worst nuclear power disaster occurred at Chernobyl in the former USSR. An explosion released about 955 kilograms of radioactive cesium-137 (137 Cs) into the atmosphere. If the half-life of 137 Cs is 30.17 years, how much will remain in the atmosphere in 191 years?
Please enter your answer as a number without the units, rounded to four decimal places.
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| 25. The biological half-life of the asthma medication theophylline is 4.5 hours for smokers. Find the amount of the drug retained in a smoker’s system 12 hours after a dose of 1 unit is taken.
Please enter your answer as a number without the units, rounded to three decimal places.
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| 26. A Wisconsin lake is stocked with 9,500 bluegill. The population is expected to grow exponentially according to the model . How many bluegill will be in the lake in 2 years?
Please enter your answer as a number without the units.
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| 27. The intensity I of light (in lumens) at a distance x meters below the surface is given by , where I0 is the intensity at the surface and k depends on the clarity of the water. At one location in the Arctic Ocean, and . Find the intensity at a depth of 3 meters.
Please enter your answer as a number without the units, rounded to two decimal places.
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| 28. A colony of 6 million bacteria is growing in a culture medium. The population P after t hours is given by the formula . Find the population after 7 hours.
Please enter your answer as an integer in number of millions without the units.
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| 29. The growth of a town’s population is modeled by . How large will the population be when ?
Please enter your answer as a number without the units, rounded to the nearest integer.
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| 30. In one individual, the percent alcohol level t minutes after two shots of whiskey is given by . Find the blood alcohol level after 14 minutes.
Please enter your answer as a number without the units, rounded to three decimal places.
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| 31. The population of the Earth is approximately 6 billion people and is growing at an annual rate of 1.2%. Assuming a Malthusian growth model, find the world population in 29 years.
Please enter your answer as a number of billions without the units, rounded to two decimal places.
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| 32. The population of the Earth is approximately 6 billion people and is growing at an annual rate of 2%. Assuming a Malthusian growth model, by what factor will the current population of the Earth increase in 31 years?
Please enter your answer as a number, rounded to two decimal places.
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| 33. The percent P of the drug triazolam (a drug for treating insomnia) remaining in a person’s bloodstream after t hours is given by . What percent will remain in the bloodstream after 10 hours?
Please enter your answer as a percent without the percent sign, rounded to three decimal places, if necessary.
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| 34. The concentration x of a certain drug in an organ after t minutes is given by Find the concentration of the drug at 10 minutes.
Please give the answer to four decimal places.
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| 35. The concentration x of a certain drug in an organ after t minutes is given by . Find the initial concentration of the drug when .
Round your answer to two decimal places, if necessary.
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| 36. In a city with a population of 1,200,000, there are currently 1000 cases of infection with the HIV virus. If the spread of the disease is projected by the formula
how many people will be infected in 7 years? Please enter your answer as a number without the units, rounded to the nearest hundred.
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| 37. The life expectancy of white females can be estimated by using the function , where x is the current age. Find the life expectancy of a white female who is currently 53 years old.
Please enter your answer as a number without the units, rounded to the nearest tenth.
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| 38. The width w (in millimeters) of successive growth spirals of the sea shell Catapulus voluto, shown in the illustration, is given by the function , where n is the spiral number. To the nearest tenth of a millimeter, find the width of the third spiral.
Please enter your answer as a number without the units.
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| 39. Before the parachute opens, the velocity v (in meters per second) of a skydiver is given by , where t is time into the jump in seconds. Find the velocity after 4 seconds.
Please enter your answer as a number without the units, rounded to two decimal places.
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| 40. In 1999, the male population of the United States was about 133 million, and the female population was about 139 million. Assuming a Malthusian growth model with a 0.9% annual growth rate, how many more females than males will there be in 17 years?
Enter your answer as a number of millions without the units, rounded to the nearest tenth.
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| Before the parachute opens, the velocity v (in meters per second) of a skydiver is given by , where t is time into the jump in seconds. After t seconds, a certain falling object has a velocity v given by . Which is falling faster after 10 seconds, this object or the skydiver?
Choose the correct letter for each question.
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41. faster
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42. slower
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| 1. Find the graph of the function.
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| 2. What does the expression equal?
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| 3. Write the equation in logarithmic form.
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| 4. Find the value of x.
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| 5. Find the value of x.
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| 6. Find the value of x.
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| 7. Find the value of x.
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| 8. Find the value of x.
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| 9. Find the value of x.
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| 10. Find the value of x.
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| 11. Find the value of x.
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| 12. Use a calculator to find the value for to four decimal places.
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| 13. Use a calculator to find a value for to four decimal places.
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| 14. Use a calculator to find the value for to four decimal places.
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| 15. Use a calculator to find y from to four decimal places.
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| 16. Use a calculator to find y to four decimal places.
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| 17. Find the value of b, if any, that would cause the graph of to look like the graph shown.
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| 18. Find the graph of the function.
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| 19. Find the graph of the function.
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| 20. Find the value of x.
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| 21. Find the value of x.
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| 22. Find the value of x.
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| 23. Find the value of x.
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| 24. Find the value of x.
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25. Use a calculator to find a value for to four decimal places.
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26. Use a calculator to find y from to four decimal places.
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27. Use a calculator to find y from to four decimal places.
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| 28. Find the value of b, if any, that would cause the graph of to look like the graph shown.
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| 29. Find the value of x.
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30. Use a calculator to find the value for to four decimal places.
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31. Use a calculator to find the value for to four decimal places.
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32. What does the expression equal?
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| 33. Find the value of x.
Please enter your answer as a fraction.
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| 34. Find the value of x.
Please enter your answer as a fraction.
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| 35. Find the value of x.
Please enter your answer as a fraction.
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| Match each equation in logarithmic form with the corresponding equation in exponential form.
Choose the correct letter for each question.
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36.
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37.
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38.
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39.
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| Match each equation in exponential form with the corresponding equation in logarithmic form.
Choose the correct letter for each question.
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40.
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41.
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42.
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| 1. An amplifier produces an output of 7 volts when the input signal is 0.15 volt. Find the decibel voltage gain. Round to the nearest whole number.
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| 2. A 8.9-volt input to a long transmission line decreases to 4.3 volts at the other end. Find the decibel voltage loss. Round to the nearest hundredths.
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| 3. Find the db gain of an amplifier whose input voltage is 1.2 volts and whose output voltage is 19 volts. Round to two decimal places, if necessary.
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| 4. Find the db gain of an amplifier whose output voltage is 3.5 volts and whose input voltage is 0.05 volts. Round to the nearest whole number.
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| 5. An earthquake has an amplitude of 4,000 micrometers and a period of 0.45 second. Find its measure on the Richter scale. Round to one decimal place, if necessary.
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| 6. An earthquake has an amplitude of 6,500 micrometers and a period of 0.065 second. Find its measure on the Richter scale. Round to one decimal place.
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| 7. An earthquake has a period of second and has an amplitude of . Find its measure on the Richter scale. Round your answer to one decimal place, if necessary.
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| 8. An earthquake has a period of second and an amplitude of . Find its measure on the Richter scale. Round your answer to one decimal place.
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| 9. If M is the theoretical maximum charge that a battery can hold and k is a positive constant that depends on the battery and the charger, the length of time (in minutes) required to charge the battery to a given level C is given by
. If , how long will it take a battery to reach a 70% charge? Assume that the battery was fully discharged when it began charging. Round your answer to the nearest tenths.
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| 10. If M is the theoretical maximum charge that a battery can hold and k is a positive constant that depends on the battery and the charger, the length of time (in minutes) required to charge the battery to a given level C is given by
If k = 0.2, how long will it take a battery to reach a 30% charge? Assume that the battery was fully discharged when it began charging. Round to one decimal place.
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| 11. A town’s population grows at the rate of 10% per year. If this growth rate remains constant, how long will it take the population to double? Round your answer to the nearest tenth.
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| 12. A population growing at an annual rate r will triple in a time t given by the formula . If the growth rate remains constant and equals 8% per year, how long will it take the population of the town to triple? Round to one decimal place.
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| 13. One mole of gas expands isothermally to triple its volume. If the gas temperature is 440K, what energy is absorbed? Round to a whole number.
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| 14. One mole of gas expands isothermally to double its volume. If the gas temperature is 360K, what energy is absorbed?
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| 15. If an investment is growing continuously for t years, its annual growth rate r is given by the
formula where P is the current value and Po is the amount originally invested. An investment of $13,400 in a particular Internet company in 1992 was worth $8,040,000 in 1998. Find this investment’s average annual growth rate during this period.
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| 16. In business, equipment is often depreciated using the double declining-balance method. In this method, a piece of equipment with a life expectancy of N years, costing $C, will depreciate to a value of $V in n years, where n is given by the formula
If a computer that cost $39,000 has a life expectancy of 4 years and has depreciated to a value of $15,000, how old is it? Round to the nearest tenth.
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| 17. In business, equipment is often depreciated using the double declining-balance method. In this method, a piece of equipment with a life expectancy of N years, costing $C, will depreciate to a value of $V in n years, where n is given by the formula
A word processor worth $470 when new had a life expectancy of 10 years. If it is now worth $130, how old is it? Round to the nearest tenth.
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| 18. If P dollars are invested at the end of each year in an annuity that earns interest at an annual rate r, the amount in the account will be A dollars after n years, where
If $2,200 is invested each year in an annuity earning 11% annual interest, when will the account be worth $25,000? Round to the nearest tenth.
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| 19. If P dollars are invested at the end of each year in an annuity that earns interest at an annual rate r, the amount in the account will be A dollars after n years, where
. If $5,000 is invested each year in an annuity earning 8% annual interest, when will the account be worth $75,000? Round to the nearest tenth.
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| 20. The coaxial power cable has a central wire with radius centimeters. It is insulated from a surrounding shield with inside radius centimeters. The maximum voltage the cable can withstand is called the breakdown voltage V of the insulation. V is given by the formula
where E is the dielectric strength of the insulation. If volts/centimeter, find V. Round your answer to the whole number.
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| 21. The deer population at a certain national park grows at a rate of 8% per year. If the current population is 130, how many years will it take for the population to reach 450? Round to the nearest hundredths.
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| 22. An earthquake with a period of second has an amplitude of 4000µm. Find its measure on the Richter scale.
Please enter your answer as a number rounded to one decimal place.
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| 23. An earthquake has a period of second and an amplitude of 35,000µm. Find its measure on the Richter scale.
Please enter your answer as a number rounded to one decimal place.
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| 24. An amplifier produces an output of 30 volts when the input signal is 0.33 volt. Find the decibel voltage gain.
Please enter your answer as a number without the units, rounded to the nearest integer.
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| 25. A 8.2-volt input to a long transmission line decreases to 4 volts at the other end. Find the decibel voltage loss.
Please enter your answer as a number without the units, rounded to two decimal places.
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| 26. Find the db gain of an amplifier whose input voltage is 0.9 volts and whose output voltage is 27 volts.
Please enter your answer as a number without the units, rounded to two decimal places.
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| 27. Find the db gain of an amplifier whose output voltage is 4.8 volts and whose input voltage is 0.5 volts.
Please enter your answer as a number without the units, rounded to the nearest integer.
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| 28. An earthquake has an amplitude of 6,000 micrometers and a period of 0.3 second. Find its measure on the Richter scale.
Please enter your answer as a number rounded to one decimal place.
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| 29. An earthquake has an amplitude of 8,500 micrometers and a period of 0.05 second. Find its measure on the Richter scale.
Please enter your answer as a number rounded to one decimal place.
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| 30. If M is the theoretical maximum charge that a battery can hold and k is a positive constant that depends on the battery and the charger, the length of time (in minutes) required to charge the battery to a given level C is given by
. If , how long will it take a battery to reach a 60% charge? Assume that the battery was fully discharged when it began charging. Please enter your answer as a number without the units, rounded to one decimal place.
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| 31. If M is the theoretical maximum charge that a battery can hold and k is a positive constant that depends on the battery and the charger, the length of time (in minutes) required to charge the battery to a given level C is given by
. If k = 0.25, how long will it take a battery to reach a 45% charge? Assume that the battery was fully discharged when it began charging. Please enter your answer as a number without the units, rounded to one decimal place.
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| 32. A town’s population grows at the rate of 12% per year. If this growth rate remains constant, how long will it take the population to double?
Please enter your answer as a number without the units, rounded to one decimal place.
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| 33. A population growing at an annual rate r will triple in a time t given by the formula . If the growth rate remains constant and equals 8% per year, how long will it take the population of the town to triple?
Please enter your answer as a number without the units, rounded to one decimal place.
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| 34. One mole of gas expands isothermically to triple its volume. If the gas temperature is 400K, what energy (in joules) is absorbed?
Please enter your answer as a number without the units, rounded to the nearest integer.
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| 35. One mole of gas expands isothermally to double its volume. If the gas temperature is 400K, what energy (in joules) is absorbed?
Please enter your answer as a number without the units, rounded to the nearest integer.
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| 36. If an investment is growing continuously for t years, its annual growth rate r is given by the formula where P is the current value and Po is the amount originally invested.
An investment of $12,400 in an Internet company in 1992 was worth $12,400,000 in 1999. Find the investment’s average annual growth rate during this period. Please enter your answer as a percent, rounded to the nearest 1 percent. __________ %
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| 37. In business, equipment is often depreciated using the double declining-balance method. In this method, a piece of equipment with a life expectancy of N years, costing $C, will depreciate to a value of $V in n years, where n is given by the formula
If a computer that cost $42,000 has a life expectancy of 5 years and has depreciated to a value of $20,000, how old is it? Please enter your answer as a number without the units, rounded to one decimal place.
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| 38. In business, equipment is often depreciated using the double declining-balance method. In this method, a piece of equipment with a life expectancy of N years, costing $C, will depreciate to a value of $V in n years, where n is given by the formula
A word processor worth $460 when new had a life expectancy of 12 years. If it is now worth $40, how old is it? Please enter your answer as a number without the units, rounded to one decimal place.
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| 39. If P dollars are invested at the end of each year in an annuity that earns interest at an annual rate r, the amount in the account will be A dollars after n years, where
If $2,900 is invested each year in an annuity earning 8% annual interest, when will the account be worth $45,000? Please enter your answer as a number without the units, rounded to one decimal place.
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| 40. If P dollars are invested at the end of each year in an annuity that earns interest at an annual rate r, the amount in the account will be A dollars after n years, where
If $6,500 is invested each year in an annuity earning 10% annual interest, when will the account be worth $55,000? Please enter your answer as a number without the units, rounded to one decimal place.
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| 41. The coaxial power cable has a central wire with radius centimeters. It is insulated from a surrounding shield with inside radius centimeters. The maximum voltage the cable can withstand is called the breakdown voltage V of the insulation. V is given by the formula
where E is the dielectric strength of the insulation. If volts/centimeter, find V. Please enter answer as a number without the units, rounded to the nearest hundred.
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| 1. Simplify the expression.
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| 2. Simplify the expression.
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| 3. Assume that x, y, and a are positive numbers. Use the properties of logarithms to write the expression in terms of the logarithms of x and y.
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| 4. Assume that x, y and a are positive numbers. Use the properties of logarithms to write the expression in terms of the logarithms of x and y.
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| 5. Assume that x, y, and b are positive numbers. Use the properties of logarithms to write the expression in terms of the logarithms of x and y.
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| 6. Assume that x, y, z and b are positive numbers. Use the properties of logarithms to write the expression in terms of the logarithms of x, y, and z.
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| 7. Assume that x is a positive number. Use the properties of logarithms to write the expression
as the logarithm of one quantity.
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| 8. Assume that x, y, and z are positive numbers. Use the properties of logarithms to write the expression as the logarithm of one quantity.
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| 9. Tell whether the statement is true or false.
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| 10. True or False?
|
| 11. True or False?
|
| 12. True or False?
|
| 13. True or False?
|
| 14. Tell whether the statement is true or false.
|
| 15. Assume that .
Use these values and the properties of logarithms to find the value . Do not use a calculator.
|
| 16. Use a calculator and the change-of-base formula to find the logarithm . Round your answer to two decimal places.
|
| 17. Use a calculator and the change-of-base formula to find the logarithm. Round your answer to four decimal places.
|
| 18. Find the pH of a solution with a hydrogen ion concentration of gram-ions per liter. Round your answer to two decimal places.
|
| 19. Find the hydrogen ion concentration of a saturated solution of calcium hydroxide whose pH is 10.3. Round your answer to three decimal places.
|
| 20. Losses in a long telephone line reduce a 20-watt input signal to an output of 4 watts. Find the db gain. (Because it is a loss, the “gain” will be negative.) Round your answer to two decimal places.
|
| 21. Simplify the expression.
|
| 22. Simplify the expression.
|
| 23. Assume that .
Use these values and the properties of logarithms to find the value . Do not use a calculator. Please give the answer to four decimal places.
|
| 24. Use a calculator and the change-of-base formula to find the logarithm.
Please give the answer to two decimal places.
|
| 25. Use a calculator and the change-of-base formula to find the logarithm.
Please give the answer to four decimal places.
|
| 26. Find the pH of a solution with a hydrogen ion concentration of gram-ions per liter.
Please give the answer to two decimal places.
|
| 27. Losses in a long telephone line reduce a 20-watt input signal to an output of 5 watts. Find the db gain. (Because it is a loss, the “gain” will be negative.)
Please give the answer to two decimal places.
|
28. Assume that x, y, and a are positive numbers. Use the properties of logarithms to write the expression in terms of the logarithms of x and y.
|
29. Assume that x, y and a are positive numbers. Use the properties of logarithms to write the expression in terms of the logarithms of x and y.
|
| 30. Assume that x, y, and d are positive numbers. Use the properties of logarithms to write the expression in terms of the logarithms of x and y.
Please enter your coefficients as fractions.
|
31. Assume that x, y, z and b are positive numbers. Use the properties of logarithms to write the expression in terms of the logarithms of x, y, and z.
|
32. Assume that x, y, and z are positive numbers. Use the properties of logarithms to write the expression as the logarithm of one quantity.
|
33. Tell whether the statement is true or false.
|
| 34. True or False?
|
| 35. True or False?
|
| 36. True or False?
|
| 37. True or False?
|
| 38. Find the hydrogen ion concentration of a saturated solution of calcium hydroxide whose pH is 10.1.
Please give the answer in the form where a is rounded to the nearest hundredth without the units.
|
| Assume that x, y, and z are positive numbers. Match the equations.
Choose the correct letter for each question.
|
39.
|
40.
|
41.
|
| 1. Solve the equation.
Round your answer to four decimal places.
|
| 2. Solve the equation.
Round your answer to four decimal places.
|
| 3. Solve the equation.
Round your answer to four decimal places.
|
| 4. Solve the equation.
|
| 5. Solve the equation.
|
| 6. Solve the equation.
|
| 7. Solve the equation.
|
| 8. Solve the equation.
|
| 9. Solve the equation.
|
| 10. An isotope of thorium, 227 Th, has a half-life of 18.4 days. How long will it take 78% of the sample to decompose? Round your answer to two decimal places.
|
| 11. A cloth fragment is found in an ancient tomb. It contains 70% of the carbon-14 (half-life is 5700 years) that it is assumed to have had initially. How old is the cloth? Round your answer to the nearest integer.
|
| 12. A bacterial culture grows according to the formula . If it takes 9 days for the culture to triple in size, how long will it take to double in size? Round your answer to the nearest tenth of a day.
|
| 13. The intensity I of a light a distance x meters beneath the surface of a lake decreases exponentially. If the light intensity at 6 meters is 76% of the intensity at the surface, at what depth (to the nearest tenth of a meter) will the intensity be 33%?
|
| 14. The rodent population in a city is currently estimated at 20,000. If it is expected to double every 3 years, when will the population reach 490,000? Round your answer to the nearest tenth of a year.
|
| 15. Water whose temperature is at 100 oC is left to cool in a room where the temperature is 30 oC. After 2 minutes, the water temperature is 88 oC. If the water temperature T is a function of time t given by
, find k. Round your answer to the nearest hundredth.
|
| 16. Find the solution of the exponential equation, correct to four decimal places.
|
| 17. Solve the exponential equation using logarithms. Give the answer in decimal form, rounding to four decimal places if necessary.
|
| 18. Solve the equation. Round your answer to four decimal places.
If the equation has more than one root, choose them all.
|
| 19. Solve the equation. Round your answer to four decimal places.
If the equation has more than one root, choose them all. (Hint: )
|
| 20. Solve the equation. Round your answer to four decimal places.
If the equation has more than one root choose them all.
|
| 21. Solve the equation.
If the equation has more than one root choose them all.
|
| 22. Solve the equation. If an answer is not exact, give the answer to four decimal places.
|
| 23. Solve the equation. If necessary, round the answer to four decimal places.
(Hint: )
|
| 24. Solve the equation.
If an answer is not exact, give the answer to four decimal places.
|
| 25. Solve the equation. If an answer is not exact, give the answer to four decimal places.
|
| 26. Solve the equation. If an answer is not exact, give the answer to four decimal places.
|
| 27. Solve the equation.
|
| 28. Solve the equation.
|
| 29. Solve the equation.
|
| 30. Solve the equation. If an answer is not exact, give the answer to four decimal places.
|
| 31. An isotope of thorium, 227Th, has a half-life of 18.4 days. How long will it take 75% of the sample to decompose (in days)?
Please enter your answer as a number without the units, rounded to the nearest tenth.
|
| 32. A cloth fragment is found in an ancient tomb. It contains 63% of the carbon-14 (half-life is 5700 years) that it is assumed to have had initially. How old is the cloth?
Round your answer to the nearest hundred years. __________ yr
|
| 33. If $500 is deposited in an account paying 7.9% annual interest, compounded semiannually, how long will it take for the account to increase to $700?
Round your answer to the nearest tenth of a year. __________ yr
|
| 34. A bacterial culture grows according to the formula . If it takes 10 days for the culture to triple in size, how long will it take to double in size? (in days)
Round your answer to the nearest tenth of a day. __________ days
|
| 35. The intensity I of a light a distance x meters beneath the surface of a lake decreases exponentially. If the light intensity at 6 meters is 83% of the intensity at the surface, at what depth will the intensity be 34% (in meters)?
Round your answer to the nearest meter. __________ meters
|
| 36. The rodent population in a city is currently estimated at 20,000. If it is expected to double every 5 years, when will the population reach 770,000?
Round your answer to the nearest tenth of a year. in about __________ years
|
| 37. Find the solution of the exponential equation, correct to four decimal places.
|
| 38. Water whose temperature is at 100 oC is left to cool in a room where the temperature is 50 oC. After 3 minutes, the water temperature is 94 oC. If the water temperature T is a function of time t given by , find k.
Round your answer to the nearest hundredth. k ≈ __________
|
| 39. Solve the equation. If an answer is not exact, give the answer to four decimal places.
If there is more than one answer, separate them with commas.
|
| 40. Solve the equation. If an answer is not exact, give the answer to four decimal places.
(Hint: ) Enter your answer(s) as numbers, and if there is more than one answer, separate them with commas.
|
| 41. Solve the equation. If an answer is not exact, give the answer to four decimal places.
Enter your answer(s) as numbers. If there is more than one answer separate them with commas.
|
| 42. Solve the equation. If an answer is not exact, give the answer to four decimal places.
If there is more than one answer, separate them with commas.
|
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.
