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Complete Test Bank With Answers
Sample Questions Posted Below
1. Use a calculator to evaluate the expression. Round your answer to four decimal places, if necessary.

2. Use a calculator to evaluate the expression. Round your answer to six decimal places.

3. Use a calculator to evaluate the expression. Round your answer to two decimal places, if necessary.

4. Use a calculator to evaluate the expression. Round your answer to two decimal places.

5. Graph the function.

6. Graph the function.

7. Graph the function.

8. Graph the function.

9. Express in the form with an appropriate value of .

10. Is the function a growth exponential or decay exponential?

11. Graph the function .

12. Given . Graph and for .

13. Let . Use a graphing utility to graph the functions and where . Identify the graphs of and below.

14. Let . Using a graphing utility, graph for and .
What effect does c have on the graphs?

15. If $1,200 is invested for x years at an annual rate of 7%, compounded quarterly, the future value that will result is
Determine the value of the investment after 8 years. Round your answer to two decimal places, if necessary.

16. We will show in the next chapter that if $P is invested for n years at an annual rate of 3% compounded continuously, the future value of the investment is given by
Use and graph this function for .

17. The percent concentration y of a certain drug in the bloodstream at any time t in minutes is given by the equation
. Graph this equation for 0 ≤ t ≤ 30.

18. The percent concentration y of a certain drug in the bloodstream at any time t in minutes is given by the equation
. Graph this function with a graphing utility. Which of the following statements best describes the situation after 10 hours?

19. A starfish population can be modeled by , where is the number of individuals at time , r is the yearly rate of growth, and t is the number of years. Sketch the graph for to when the growth rate is 2.1% and is 5.5 billion. All numbers on the vertical axis are in billions.

20. The following figure, from Investor’s Business Daily (March 5, 1998), shows how quickly the U.S. metal processing industry isconsolidating. The linear equation that is the best fit for the number of metal processors as a function of years after 1990 is , and the best exponential fit is . The linear equation seems to give a much better fit for the data points than the exponential equation. Why then is the exponential equation a more useful model to predict the number of metal processors in ?

21. Total personal income in the United States (in billions of dollars) for selected years from 1960 to 2002 is given in the following table.
Source: Bureau of Economic Analysis, U.S. Department of Commerce These data can be modeled by an exponential function. Write the equation of this function, with x as the number of years past 1960. If it’s necessary round your calculations to four decimal places.

22. Total personal income in the United States (in billions of dollars) for selected years from 1960 to 2002 is given in the following table.
Source: Bureau of Economic Analysis, U.S. Department of Commerce
These data can be modeled by an exponential function. Write the equation of this function, with x as the number of years past 1960. If this model is accurate, what will be the total U.S. personal income in 2010? Round your answer to two decimal places.

23. The consumer price index (CPI) is calculated by averaging the prices of various items after assigning a weight to each item. The following table gives the consumer price indexes for selected years from 1940 through 2002, reflecting buying patterns of all urban consumers, with x representing years past 1900. Find an equation that models these data. If it’s necessary, round your calculations to four decimal places.
Source: U.S. Bureau of the Census

24. The consumer price index (CPI) is calculated by averaging the prices of various items after assigning a weight to each item. The following table gives the consumer price indexes for selected years from 1940 through 2002, reflecting buying patterns of all urban consumers. Find an equation that models these data and use it to predict the consumer price index in 2015. Use the model to predict the consumer price index in 2015. Round your answer to two decimal places.
Source: U.S. Bureau of the Census

25. The consumer price index (CPI) is calculated by averaging the prices of various items after assigning a weight to each item. The following table gives the consumer price indexes for selected years from 1940 through 2002, reflecting buying patterns of all urban consumers. Find an equation that models these data and use it to determine when the consumer price index will pass 349.
Source: U.S. Bureau of the Census

26. The following table gives the average number of students per computer in public schools for the school years that ended in 1985 through 2002. Let x be the number of years past 1980. Find an exponential model for these data. Round your answer to three decimal places.
Source: Quality Education Data, Inc., Denver, Colorado

27. The following table gives the average number of students per computer in public schools for the school years that ended in 1985 through 2002. Find an exponential model for these data. How many students per computer in public schools does this model predict for 2005? Round your answer to two decimal places.
Source: Quality Education Data, Inc., Denver, Colorado

28. Write the equation in exponential form.

29. Write the equation in exponential form.

30. Solve for x by writing the equation in exponential form. Round your answer two decimal places, if necessary.

31. Solve for x by writing the equation in exponential form. Round your answer to two decimal places, if necessary.

32. Solve for x by writing the equation in exponential form.

33. Write the equation in logarithmic form.

34. Write the equation in logarithmic form.

35. Graph the function.

36. Graph the function.

37. Use properties of logarithms or a definition to simplify the expression. Check the result with a changeofbase formula and a calculator. Round your answer two decimal places.

38. Use properties of logarithms or a definition to simplify the expression. Check the result with a changeofbase formula and a calculator.

39. Use properties of logarithms or a definition to simplify the expression.
If find .

40. Use properties of logarithms or a definition to simplify the expression.
If , find .

41. Use properties of logarithms or a definition to simplify the expression.
If , find .

42. Evaluate the logarithm by using properties of logarithms and the following facts. Round your answer two decimal places.

43. Evaluate the logarithm by using properties of logarithms and the following facts. Round your answer to two decimal places.

44. Evaluate the logarithm by using properties of logarithms and the following fact. Round your answer two decimal places.

45. Evaluate the logarithm by using properties of logarithms and the following facts. Round your answer two decimal places.

46. Write the expression as the sum or difference of two logarithmic functions containing no exponents.

47. Write the expression as the sum or difference of two logarithmic functions containing no exponents.

48. Use the properties of logarithms to write the expression as a single logarithm.

49. Use the properties of logarithms to write the expression as a single logarithm.

50. Use a calculator to determine whether expression (a) is equivalent to expression (b).

51. Use a calculator to determine whether expression (a) is equivalent to expression (b).

52. Given , use a graphing calculator to graph for and .

53. Use a changeofbase formula to evaluate with a calculator or other technology. Round your answer to four decimal places.

54. Find an equivalent expression for the given logarithm using the changeofbase formula.

55. Use a changeofbase formula to rewrite the logarithm in terms of natural logarithms.

56. Which answer choice is a graph of the function?

57. Use the formula .
In October 2004, an earthquake measuring 6.8 on the Richter scale occurred in Japan. The largest quake in Japan since 1990 was one in 1993 that registered 7.7. How many times more severe was the 1993 shock than the one in 2004 on the Richter scale? Round your answer to one decimal place.

58. Use the formula .
The San Francisco earthquake of 1906 measured 8.25 on the Richter scale, and the San Francisco earthquake of 1989 measured 7.1. How much more intense was the 1906 quake?

59. Use the fact that the loudness of sound (in decibels) perceived by the human ear depends on intensity levels according to , where is the threshold of hearing for the average human ear. Find the loudness when I is 1,000 times .

60. Use the following information. Chemists use the pH (hydrogen potential) of a solution to measure its acidity or basicity. The pH is given by the formula , where is the concentration of hydrogen ions in moles per liter. What value of is associated with pH level 12?

61. Use the formula to find the doubling time t, in years, for an investment at r% compounded n times per year. Suppose you make an investment of $1,300 at interest rate 11% compounded quarterly. How long will it take for your investment to double? Round your answer to two decimal places.

62. Between the years 1960 and 2002, the percent of women in the work force is given by , where x is the number of years past 1950 (Source: U.S. Bureau of Labor Statistics). What does this model estimate to be the percent of women in the work force in 2019? Round your answer to two decimal places.

63. Between the years 1960 and 2002, the percent of women in the work force is given by , where x is the number of years past 1950 (Source: U.S. Bureau of Labor Statistics). Graph this function with a graphing utility and use the graph drawn to estimate the year in which the percent reached 50. Round your answer to the nearest year.

64. Solve the exponential equation. Round your answer to three decimal places, if necessary.

65. Solve the exponential equation. Give answers correct to 3 decimal places.

66. Solve the exponential equation. Give the answer correct to 3 decimal places.

67. Solve the exponential equation. Give the answer correct to 3 decimal places.

68. Solve the exponential equation. Give the answer correct to 3 decimal places.

69. Solve the logarithmic equation . Round your answer to three decimal places.

70. Solve the logarithmic equation . Round your answer to three decimal places.

71. Solve the logarithmic equation .

72. The monthly sales S for a product is given by , where x is the number of months that have passed since the end of a promotional campaign. Determine the monthly sales 4 months after the promotional campaign. Round your answer to the nearest cent.

73. The monthly sales S for a product is given by , where x is the number of months that have passed since the end of a promotional campaign. How many months after the end of the campaign will sales drop below 6,000, if no new campaign is initiated? Round to two decimal places.

74. The purchasing power P (in dollars) of an annual amount of A dollars after t years of 4% inflation decays according to . How long will it be before a pension of $60,000 per year has a purchasing power of $30,000? Round your answer to one decimal place.

75. The purchasing power P (in dollars) of an annual amount of A dollars after t years of 4% inflation decays according to . Determine how large a pension A needs to be so that the purchasing power P is $70,000 after 25 years? Round your answer to the nearest dollar.

76. An initial amount of 300 g of the radioactive isotope thorium234 decays according to , where t is in years. How long does it take for half of the initial amount to disintegrate? This time is called the halflife of this isotope. Round your answer to one decimal place.

77. The population y of a certain country was 100,000 in 1990 and 149,182 in 2000. Assume the formula applies to the growth of the country’s population. Estimate the population of the country in 2010. Round your answer to the nearest human.

78. For selected years from 1960 to 2001, the national health care expenditures H, in billions of dollars, can be modeled by , where t is the number of years past 1960 (Source: U.S. Department of Health and Human Services). If this model remains accurate, in what year will national health care expenditures reach $3 trillion (that is, $3000 billion)? Round your answer to the nearest year.

79. The demand function for a certain commodity is given by , where q is number of units. At what price per unit will the quantity demanded equal 6 units? Round your answer to the nearest cent.

80. The demand function for a certain commodity is given by , where q is number of units. If the price is $1.11 per unit, how many units will be demanded, to the nearest unit?

81. If the supply function for a product is given by , where q represents the number of hundreds of units, what will be the price when the producers are willing to supply 200 units? Round your answer to the nearest cent.

82. If the total cost function for a product is , where x is the number of items produced, what is the total cost of producing 50 units? Round your answer to the nearest cent.

83. If the total cost (in dollars) for x units of a product is given by , what is the total cost of producing 150 units? Round your answer to the nearest cent.

84. If the demand function for a product is given by where p is the price per unit when x units are demanded, what is the total revenue when 90 units are demanded and supplied? Round your answer to the nearest cent.

85. If $7,000 is invested at an annual rate of 11.5% compounded continuously, the future value S at any time t (in years) is given by . What is the amount after 12 months? Round your answer to the nearest cent.

86. If $4,500 is invested at an annual rate of 8% compounded continuously, the future value S at any time t (in years) is given by . How long does it take for the investment to double? Round your answer to one decimal place.

87. If $6,000 is invested at an annual rate of 9% per year compounded monthly, the future value S at any time t (in months) is given by . What is the amount after 1 year? Round your answer to the nearest cent.

88. If $9,000 is invested at an annual rate of 11% per year compounded monthly, the future value S at any time t (in months) is given by . How long does it take for the investment to double? Round your answer to one decimal place.

89. The securities industry experienced dramatic growth in the last two decades of the 20th century. The following models for the industry’s revenue R and expenses or costs C (both in billions of dollars) were developed as functions of the years past 1980 with data from the U.S. Securities and Exchange Commission’s 2000 Annual Report (2001). and . Use the models to predict the profit for the securities industry in 2009. Round your answer to two decimal places.

90. By using data from the U.S. Bureau of Labor Statistics for the years 1968–2002, the purchasing power P of a 1983 dollar can be modeled with the function , where t is the number of years past 1960. Based on this model, what is the purchasing power of a 1983 dollar in the year 1970? Round your answer to the nearest cent.

91. By using data from the U.S. Bureau of Labor Statistics for the years 1968–2002, the purchasing power P of a 1983 dollar can be modeled with the function , where t is the number of years past 1960. In what year will the purchasing power of a 1983 dollar be $0.20? Roundup your answer to the nearest year.

92. Suppose the supply of x units of a product at price p dollars per unit is given by . How many units would be supplied when the price is $50 each? Round your answer to one decimal place.

93. The president of a company predicts that sales N will increase after she assumes office and that the number of monthly sales will follow the curve given by , where t represents time in months since she assumed office. What will the sales be when she assumes office?

94. The president of a company predicts that sales N will increase after she assumes office and that the number of monthly sales will follow the curve given by , where t represents time in months since she assumed office. What is the expected upper limit on sales?

95. The president of a company predicts that sales N will increase after she assumes office and that the number of monthly sales will follow the curve given by , where t represents time in months since she assumed office. What will be the sales after 9 months? Round your answer to the nearest month.

96. Suppose that the equation represents the number of employees working t years after a company begins operations. How many employees are there when the company opens (at t = 0)?

97. Suppose that the equation represents the number of employees working t years after a company begins operations. After how many years will at least 300 employees be working? Round your answer to two decimal places.

98. The concentration y of a certain drug in the bloodstream t hours after an oral dosage (with ) is given by the equation . What is the concentration after 6 hours? Round your answer to one decimal place.

99. The concentration y of a certain drug in the bloodstream t hours after an oral dosage (with ) is given by the equation How long does it take for the concentration to reach 90? Round your answer to two decimal places.

100. On a college campus of 10,000 students, a single student returned to campus infected by a disease. The spread of the disease through the student body is given by , where y is the total number infected at time t (in days). How many are infected after 7 days?

101. On a college campus of 10,000 students, a single student returned to campus infected by a disease. The spread of the disease through the student body is given by , where y is the total number infected at time t (in days). The school will shut down if 50% of the students are ill. What value of t corresponds to this percentage?

102. Suppose that the market share y (as a percent) that a company expects t months after a new product is introduced is given by . What is the market share after the first month (to the nearest percent)? Round your answer to two decimal place.

103. Suppose that the market share y (as a percent) that a company expects t months after a new product is introduced is given by . How long (to the nearest month) will it take for the market share to be 25%? Round your answer to one decimal place.

104. Pollution levels in Lake Erie have been modeled by the equation , where x is the volume of pollutants (in cubic kilometers) and t is the time (in years) (Adapted from R. H. Rainey, Science 155 (1967), 1242–1243). Find the initial pollution level; that is, find x when t=0.

105. For selected years from 1978 to 2002, the number of mutual funds N, excluding money market funds, can be modeled by , where t is the number of years past 1975 (Source: Investment Company Institute, Mutual Fund Fact Book (2003)). Use the model to estimate the number of mutual funds in 2004. Round your answer to the nearest whole number.

106. For selected years from 1978 to 2002, the number of mutual funds N, excluding money market funds, can be modeled by , where t is the number of years past 1975 (Source: Investment Company Institute, Mutual Fund Fact Book (2003)). Use the model to estimate the year when the number of mutual funds will reach 8,000.

107. The following table gives the percent of the U.S. population with Internet connections for the years 1997 to 2003. Use a calculator to find the logistic function that models these data. Use x as the number of years past 1995.
Source: U.S. Department of Commerce

108. The following table gives the percent of the U.S. population with Internet connections for the years 1997 to 2003. Use a calculator to find the logistic function that models these data and then use the model to predict the percent of the U.S. population with Internet connections in 2015. Use x as the number of years past 1995. Round your answer to one decimal place.
Source: U.S. Department of Commerce

109. The following table gives the percent of the U.S. population with Internet connections for the years 1997 to 2003. Use a calculator to find the logistic function that models these data and then use the model to predict when 59.4% of the U.S. population will have internet connections. Use x as the number of years past 1995. Round your answer to the nearest year.
Source: U.S. Department of Commerce

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