Description
Calculus An Applied Approach, 9th Edition, Test Bank – Ron Larson
SAMPLE
Chapter 4
Ch04 Expo and Log Functions Download Sample
Solution Sample Chapter 4
1. 
Evaluate the expression . 
A) 
243 
B) 
3 
C) 
9 
D) 
11 
E) 
13 
Ans: 
C 
2. 
Use the properties of exponents to simplify the expression . 
A) 

B) 
25 
C) 

D) 

E) 
625 
Ans: 
D 
3. 
After t years, the remaining mass y(in grams) of 20 grams of a radioactive element whose halflife is 35 years is given by , for . How much of the initial mass remains after 140 years? Round your answer to two decimal places. 
A) 
2.50 grams 
B) 
2.45 grams 
C) 
3.55 grams 
D) 
3.40 grams 
E) 
1.25 grams 
Ans: 
E 
4. 
Sketch the graph of the function . 

A) 


B) 


C) 


D) 


E) 


Ans: 
B 
5. 
With an annual rate of inflation of 4% over the next 10 years, the approximate cost of goods or services during any year in the decade is given by where is the time (in years) and is the present cost. The price of an oil change for a car is presently $24.95.Estimate the price 10 years from now. 
A) 
$37.09 
B) 
$36.93 
C) 
$89.00 
D) 
$63.90 
Ans: 
B 
6. 
Use a graphing utility to graph the function . 

A) 


B) 


C) 


D) 


E) 


Ans: 
C 
7. 
Use a graphing utility to graph the function . 

A) 


B) 


C) 


D) 


E) 


Ans: 
B 
8. 
Assume the population P (in millions) of the United States from 1992 through 2005 can be modeled by the exponential function , where t is the time in years, with t = 2 corresponding to1992. Use the model to estimate the population in the year 2007. Round your answer to the nearest million. 
A) 
7022 million 
B) 
4372 million 
C) 
11,277 million 
D) 
657 million 
E) 
7021 million 
Ans: 
A 
9. 
After t years, the value of a car that originally cost 19,000 depreciates so that each year it is worth of its value for the previous year. Find a model for V(t), the value of the car after t years. 
A) 
V(t) = 19,000 
B) 
V(t) = 19,000^{t} 
C) 
V(t) = 19,000 
D) 
V(t) = 19,000 
E) 
V(t) = 19,000^{t} 
Ans: 
C 
10. 
Suppose that the annual rate of inflation averages 4% over the next 10 years. With this rate of inflation, the approximate cost C of goods or services during any year in that decade will be given by C(t) = P(1.04)^{t}, 010 where t is time in years and P is the present cost. If the price of an oil change for your car is presently 22.95, estimate the price 9 years from now. Round your answer to two decimal places. 
A) 
33.97 
B) 
34.67 
C) 
35.97 
D) 
37.67 
E) 
32.67 
Ans: 
E 
11. 
Use the properties of exponents to simplify the expression . 
A) 

B) 

C) 

D) 

E) 

Ans: 
C 
12. 
Sketch the graph of the function . 

A) 


B) 


C) 


D) 


E) 


Ans: 
B 
13. 
Sketch the graph of the function . 

A) 


B) 


C) 


D) 


E) 


Ans: 
C 
14. 
Use a graphing utility to graph the function . Be sure to choose an appropriate viewing window. 

A) 


B) 


C) 


D) 


E) 


Ans: 
A 
15. 
Determine whether the function below has any horizontal asymptotes. 
A) 
horizontal asymptotes: y = 1 
B) 
no horizontal asymptotes 
C) 
horizontal asymptotes: y = 0 and y = 2 
D) 
horizontal asymptotes: y = 3 
E) 
horizontal asymptotes: y = 1 and y = 3 
Ans: 
B 
16. 
Determine the continuity of the function below. 
A) 
discontinuous at x = 0 
B) 
continuous on the entire real number line 
C) 
discontinuous at x = 1 
D) 
discontinuous at x = 2 
E) 
discontinuous at x = 4 
Ans: 
B 
17. 
What is the resulting balance if $6800 is invested for 5 years at an annual rate of 12% compounded monthly? 
A) 
7146.87 
B) 
7662.41 
C) 
10,880.00 
D) 
12,353.54 
E) 
40,062.90 
Ans: 
D 
18. 
How much more interest will be earned if $4000 is invested for 7 years at an annual rate of 12% compounded continuously, instead of at 12% compounded quarterly? 
A) 
$38.58 
B) 
$75.18 
C) 
$113.76 
D) 
$1791.71 
E) 
$1866.89 
Ans: 
C 
19. 
What lump sum should be deposited in an account that will earn at an annual rate of 10%, compounded quarterly, to grow to $180,000 for retirement in 35 years? 
A) 
$177,957.47 
B) 
$5514.93 
C) 
$12,000.00 
D) 
$40,000.00 
E) 
$5674.55 
Ans: 
E 
20. 
To help their son buy a car on his 18th birthday, a boy’s parents invest $1600 on his 12th birthday. If the investment pays an annual rate of 11% compounded continuously, how much is available on his 18th birthday? 
A) 
$3068.20 
B) 
$3095.67 
C) 
$2992.66 
D) 
$2656.00 
E) 
$22,421.13 
Ans: 
B 
21. 
What is the annual percentage yield (or effective annual rate) for a nominal rate of 8.1% compounded quarterly? 
A) 
8.10% 
B) 
8.41% 
C) 
8.44% 
D) 
8.35% 
E) 
8.26% 
Ans: 
D 
22. 
Find the future value if $2900 is invested for 4 years at an annual rate of 10% compounded quarterly. 
A) 
4640.00 
B) 
4284.62 
C) 
3201.06 
D) 
4245.89 
E) 
4305.07 
Ans: 
E 
23. 
The demand function for a product is modeled by . Find the price of the product if the quantity demanded is x = 200. Round your answer to two decimal places where applicable. 
A) 
547.90 
B) 
2282.47 
C) 
727.73 
D) 
738.03 
E) 
2272.27 
Ans: 
C 
24. 
The demand function for a product is modeled by . What is the limit of the price as x increases without bound? Round your answer to two decimal places where applicable. 
A) 
The limit of the price as x increases without bound is 1. 
B) 
The limit of the price as x increases without bound is 1. 
C) 
The limit of the price as x increases without bound is 0. 
D) 
The limit of the price as x increases without bound is . 
E) 
The limit of the price as x increases without bound is . 
Ans: 
C 
25. 
The average time between incoming calls at a switchboard is 3 minutes. If a call has just come in, the probability that the next call will come within the next t minutes is . Find the probability that the next call will come within the next minute. Round your answer to two decimal places. 
A) 
4.08% 
B) 
0.41% 
C) 
195.92% 
D) 
6.31% 
E) 
3.95% 
Ans: 
A 
26. 
Find the derivative of 
A) 

B) 

C) 

D) 

E) 

Ans: 
C 
27. 
Find the derivative of the following function. 
A) 

B) 

C) 

D) 

E) 

Ans: 
E 
28. 
Find the derivative of the following function. 
A) 

B) 

C) 

D) 

E) 

Ans: 
A 
29. 
Find the derivative of the following function. 
A) 

B) 

C) 

D) 

E) 

Ans: 
B 
30. 
Find if . 
A) 

B) 

C) 

D) 

E) 

Ans: 
E 
31. 
Find the derivative of the following function. 
A) 

B) 

C) 

D) 

E) 

Ans: 
A 
32. 
Find the derivative of the following function. 
A) 

B) 

C) 

D) 

E) 

Ans: 
A 
33. 
Find if . 
A) 

B) 

C) 

D) 

E) 

Ans: 
C 
34. 
Find the equation of the tangent line to at the point (0,1). 
A) 

B) 

C) 

D) 

E) 

Ans: 
D 
35. 
Find an equation of the tangent line to the graph of at the point (0,1) . 
A) 

B) 

C) 

D) 

E) 

Ans: 
D 
36. 
Write the equation of the line tangent to the graph of at 
A) 

B) 

C) 

D) 

E) 

Ans: 
D 
37. 
If 
A) 

B) 

C) 

D) 

E) 

Ans: 
C 
38. 
If 
A) 

B) 

C) 

D) 

E) 

Ans: 
B 
39. 
Use implicit differentiation to find . 
A) 

B) 

C) 

D) 

E) 

Ans: 
D 
40. 
If 
A) 

B) 

C) 

D) 

E) 

Ans: 
A 
41. 
Find if . 
A) 

B) 

C) 

D) 

E) 

Ans: 
E 
42. 
Find the extrema of the function . 
A) 
(0, 1) 
B) 
, (0, 0) 
C) 

D) 
no relative extrema 
E) 

Ans: 
D 
43. 
Find the extrema of the function by analyzing its graph below. 
A) 
(0, 1) 
B) 
no relative extrema 
C) 
, (0, 0) 
D) 

E) 

Ans: 
B 
44. 
Solve for the equation for . 
A) 

B) 

C) 

D) 

E) 

Ans: 
D 
45. 
The average typing speed N (in words per minute) after t weeks of lessons is modeled by . Find the rate at which the typing speed is changing when t = 20 weeks. Round your answer to two decimal places. 
A) 
1.75 words/min/week 
B) 
2.36 words/min/week 
C) 
2.85 words/min/week 
D) 
4.59 words/min/week 
E) 
5.38 words/min/week 
Ans: 
B 
46. 
Future value. The future value that accrues when $500 is invested at 5%, compounded continuously, is , where t is the number of years. At what rate is the money in this account growing when 
A) 
$7.10 per year 
B) 
$26.81 per year 
C) 
$709.53 per year 
D) 
$517.81 per year 
E) 
$35.48 per year 
Ans: 
E 
47. 
A survey of high school seniors from a certain school district who took the SAT has determined that the mean score on the mathematics portion was 500 with a standard deviation of 13.5. Assuming the data can be modeled by a normal probability density function, find a model for these data. 
A) 

B) 

C) 

D) 

E) 

Ans: 
D 
48. 
A survey of high school seniors from a certain school district who took the SAT has determined that the mean score on the mathematics portion was 650 with a standard deviation of 13.5. By a normal probability density function the data can be modeled as . Find the derivative of the model. 
A) 

B) 

C) 

D) 

E) 

Ans: 
B 
49. 
Write the logarithmic equation as an exponential equation. 
A) 

B) 

C) 

D) 

E) 

Ans: 
C 
50. 
Write the exponential equation as a logarithmic equation. 
A) 

B) 

C) 

D) 

E) 

Ans: 
A 
51. 
Sketch the graph of the function . 

A) 


B) 


C) 


D) 


E) 


Ans: 
E 
52. 
Sketch the graph of the function . 

A) 


B) 


C) 


D) 


E) 


Ans: 
A 
53. 
Sketch the graph of the function . 

A) 


B) 


C) 


D) 


E) 


Ans: 
B 
54. 
Simplify 
A) 

B) 

C) 

D) 

E) 

Ans: 
A 
55. 
Simplify . 
A) 

B) 

C) 

D) 

E) 

Ans: 
D 
56. 
Use the properties of logarithms to approximate given that and 
A) 
–6.0088 
B) 
–1.2130 
C) 
0.6641 
D) 
8.6586 
E) 
6.0088 
Ans: 
B 
57. 
Use the properties of logarithms to expand 
A) 

B) 

C) 

D) 

E) 
none of the above 
Ans: 
B 
58. 
Use the properties of logarithms to expand . 
A) 

B) 

C) 

D) 

E) 

Ans: 
E 
59. 
Use the properties of logarithms to write the expression as a sum, difference, or multiple of logarithms. 
A) 

B) 

C) 

D) 

E) 

Ans: 
C 
60. 
Use the properties of logarithms to write the expression as a single logarithm. 
A) 

B) 

C) 

D) 

E) 

Ans: 
A 
61. 
Write the expression as the logarithm of a single quantity. 
A) 

B) 

C) 

D) 

E) 

Ans: 
D 
62. 
Write the expression as the logarithm of a single quantity. 
A) 

B) 

C) 

D) 

E) 

Ans: 
E 
63. 
Write the following expression as a logarithm of a single quantity. 
A) 

B) 

C) 

D) 

E) 
none of the above 
Ans: 
B 
64. 
Write the following expression as a logarithm of a single quantity. 
A) 

B) 

C) 

D) 

E) 

Ans: 
D 
65. 
Solve the following equation for accurate to three decimal places. 
A) 

B) 

C) 

D) 

E) 

Ans: 
C 
66. 
Solve the following equation for accurate to three decimal places. 
A) 

B) 

C) 

D) 

E) 

Ans: 
B 
67. 
Solve the exponential equation. Give the answer correct to 3 decimal places. 
A) 
0.735 
B) 
1.471 
C) 
2.719 
D) 
1.242 
E) 
4.970 
Ans: 
E 
68. 
Solve the exponential equation. Give the answer correct to 3 decimal places. 
A) 
–0.243 
B) 
17.028 
C) 
2.704 
D) 
–17.028 
E) 
–2.173 
Ans: 
C 
69. 
Solve the exponential equation. Give the answer correct to 3 decimal places. 
A) 
–2.734 
B) 
–0.130 
C) 
1.841 
D) 
–0.921 
E) 
5.468 
Ans: 
E 
70. 
Solve the exponential equation. Give answers correct to 3 decimal places. 
A) 
216 
B) 
0.571 
C) 
0.774 
D) 
0.371 
E) 
108 
Ans: 
B 
71. 
Solve the following equation foraccurate to three decimal places. 
A) 

B) 

C) 

D) 

E) 

Ans: 
D 
72. 
Solve for t. Round your answer to four decimal places. 
A) 
1.1772 
B) 
0.2942 
C) 
2.5673 
D) 
0.2943 
E) 
2.4502 
Ans: 
D 
73. 
How long (in years) would $400 have to be invested at an annual rate of 10%, compounded continuously, to amount to $530? 
A) 
3.25 years 
B) 
2.95 years 
C) 
0.56 years 
D) 
4.54 years 
E) 
2.81 years 
Ans: 
E 
74. 
Find the derivative of the following function. 
A) 

B) 

C) 

D) 

E) 

Ans: 
B 
75. 
Find the derivative of the following function. 
A) 

B) 

C) 

D) 

E) 

Ans: 
A 
76. 
Find the derivative of the following function. 
A) 

B) 

C) 

D) 

E) 

Ans: 
A 
77. 
Find the derivative of 
A) 

B) 

C) 

D) 

E) 

Ans: 
B 
78. 
Find the derivative of the following function. 
A) 

B) 

C) 

D) 

E) 

Ans: 
D 
79. 
Find the derivative of the following function. 
A) 

B) 

C) 

D) 

E) 

Ans: 
D 
80. 
Find the derivative of the following function. 
A) 

B) 

C) 

D) 

E) 

Ans: 
C 
81. 
Find the derivative of the function . 
A) 

B) 

C) 

D) 

E) 

Ans: 
D 
82. 
Find the derivative of the function . 
A) 

B) 

C) 

D) 

E) 

Ans: 
E 
83. 
Find the derivative of the function . 
A) 

B) 

C) 

D) 

E) 

Ans: 
D 
84. 
Find . 
A) 

B) 

C) 

D) 

E) 

Ans: 
A 
85. 
Find . 
A) 

B) 

C) 

D) 

E) 

Ans: 
C 
86. 
Find . 
A) 

B) 

C) 

D) 

E) 

Ans: 
A 
87. 
Find . 
A) 

B) 

C) 

D) 

E) 

Ans: 
C 
88. 
Find . 
A) 

B) 

C) 

D) 

E) 

Ans: 
D 
89. 
Find if 
A) 

B) 

C) 

D) 

E) 

Ans: 
B 
90. 
Find . 
A) 

B) 

C) 

D) 

E) 

Ans: 
A 
91. 
Find if 
A) 

B) 

C) 

D) 

E) 

Ans: 
B 
92. 
Find . 
A) 

B) 

C) 

D) 

E) 

Ans: 
E 
93. 
Use a changeofbase formula to rewrite the logarithm in terms of natural logarithms. 
A) 

B) 

C) 

D) 

E) 

Ans: 
E 
94. 
Use a calculator to evaluate the logarithm . Round your answer to three decimal places. 
A) 
0.197 
B) 
2.444 
C) 
6.360 
D) 
3.717 
E) 
5.087 
Ans: 
E 
95. 
Find . 
A) 

B) 

C) 

D) 

E) 

Ans: 
A 
96. 
Find the derivative of the following function. 
A) 

B) 

C) 

D) 

E) 

Ans: 
B 
97. 
Find . 
A) 

B) 

C) 

D) 

E) 

Ans: 
E 
98. 
Find if . 
A) 

B) 

C) 

D) 

E) 

Ans: 
C 
99. 
For , calculate to three decimal places. 
A) 
1.609 
B) 
–40.236 
C) 
–13.047 
D) 
–1.000 
E) 
–8.047 
Ans: 
C 
100. 
Find an equation of the tangent line to the graph of at the point . 
A) 

B) 

C) 

D) 

E) 
none of the above 
Ans: 
C 
101. 
If 
A) 

B) 

C) 

D) 

E) 

Ans: 
A 
102. 
Write the equation of the line tangent to the curve 
A) 

B) 

C) 

D) 

E) 

Ans: 
D 
103. 
Find the second derivative of the function . 
A) 

B) 

C) 

D) 

E) 

Ans: 
B 
104. 
Find the second derivative of the function . 
A) 

B) 

C) 

D) 

E) 

Ans: 
C 
105. 
The relationship between the number of decibels and the intensity of a sound I in watts per square centimeter is given by . Find the rate of change in the number of decibels when the intensity is watt per square centimeter. Round your answer to the nearest decibel. 
A) 
434 decibels per watt per square cm 
B) 
43,429 decibels per watt per square cm 
C) 
4343 decibels per watt per square cm 
D) 
434,294 decibels per watt per square cm 
E) 
4345 decibels per watt per square cm 
Ans: 
C 
106. 
Find the relative minima, and use a graphing utility to check your results. 
A) 

B) 

C) 

D) 

E) 
does not exist 
Ans: 
E 
107. 
Find the relative maxima, and use a graphing utility to check your results. 
A) 

B) 

C) 

D) 

E) 
does not exist 
Ans: 
B 
108. 
Locate any relative extrema and inflection points of the function . Use a graphing utility to confirm your results. 
A) 
relative maximum value at ; inflection point at x = 0 
B) 
relative minimum value at ; inflection point at x = 0 
C) 
relative minimum value at ; no inflection points 
D) 
relative minimum value at ; no inflection points 
E) 
relative maximum value at ; no inflection points 
Ans: 
D 
109. 
Locate any relative extrema and inflection points of the function . 
A) 
no relative extrema; inflection point at 
B) 
relative maximum at ; inflection point at 
C) 
relative minimum at ; inflection point at 
D) 
no relative extrema; inflection point at 
E) 
relative minimum at ; no inflection points 
Ans: 
E 
110. 
Locate any relative extrema and inflection points of the function . 
A) 
relative minimum at ; inflection point at 
B) 
relative minimum at ; no inflection points 
C) 
no relative maximum or minimum; inflection point at 
D) 
no relative extrema or inflection points. 
E) 
relative maximum at ; inflection point at 
Ans: 
A 
111. 
Find the yvalue at the relative minima, and use a graphing utility to check your result. 
A) 

B) 

C) 

D) 

E) 
does not exist 
Ans: 
A 
112. 
The cost of producing x units of a product is modeled by . Find the average cost function . 
A) 

B) 

C) 

D) 

E) 

Ans: 
C 
113. 
The cost of producing x units of a product is modeled by . Find the minimum average cost analytically. Round your answer to two decimal places. 
A) 
200.00 dollars per unit 
B) 
199.40 dollars per unit 
C) 
199.18 dollars per unit 
D) 
201.41 dollars per unit 
E) 
199.28 dollars per unit 
Ans: 
C 
114. 
Find the exponential function that passes through the two given points and . 
A) 

B) 

C) 

D) 

E) 

Ans: 
D 
115. 
Use the given information to write an equation for y. 
A) 

B) 

C) 

D) 

E) 

Ans: 
B 
116. 
Carbon14(^{14}C) dating assumes that the carbon on the Earth today has the same radioactive content as it did centuries ago. If this is true, then the amount of ^{14}C absorbed by a tree that grew several centuries ago should be the same as the amount of ^{14}C absorbed by a similar tree today. A piece of ancient charcoal contains only 18% as much of the radioactive carbon as a piece of modern charcoal. How long ago was the tree burned to make the ancient charcoal? (The halflife of ^{14}C is 5715 years.) Round your answer to the nearest integer. 
A) 
2,310 years 
B) 
33,123 years 
C) 
2,315 years 
D) 
14,139 years 
E) 
14,144 years 
Ans: 
D 
117. 
The number of a certain type of bacteria increases continuously at a rate proportional to the number present. There are 200 present initially, and 400 present 7 hours later. How many will there be 20 hours after the initial time? Round your answer to the nearest integer. 
A) 
28 bacteria 
B) 
1344 bacteria 
C) 
1449 bacteria 
D) 
41 bacteria 
E) 
36 bacteria 
Ans: 
C 
118. 
The effective yield is the annual rate i that will produce the same interest per year as the nominal rate compounded n times per year. For a rate that is compounded n times per year, the formula for effective yield is given as . Find the effective yield for a nominal rate of 6%, compounded monthly. Round your answer to two decimal places. 
A) 
0.62% 
B) 
6.41% 
C) 
6.80% 
D) 
1.18% 
E) 
6.17% 
Ans: 
E 
119. 
The cumulative sales (in thousands of units) of a new product after it has been on the market for t years may be modeled by . During the first year, 5000 units were sold. What is the saturation point for this product? How many units will be sold after 6 years? 
A) 
The saturation point for the market is 3000 units and 19,953 units will be sold after 6 years. 
B) 
The saturation point for the market is 30,000 units and 27,366 units will be sold after 6 years. 
C) 
The saturation point for the market is 30,000 units and 19,953 units will be sold after 6 years. 
D) 
The saturation point for the market is 30,000 units and 20,076 units will be sold after 6 years. 
E) 
The saturation point for the market is 3000 units and 27,366 units will be sold after 6 years. 
Ans: 
C 
120. 
Use the given information to write an exponential equation for y. Does the function represent exponential growth or exponential decay? 
A) 

B) 

C) 

D) 

Ans: 
B 
121. 
What percent of a present amount of radioactive radium will remain after 900 years? 
A) 
45% 
B) 
25% 
C) 
65% 
D) 
68%. 
Ans: 
D 
122. 
The management of a factory finds that the maximum number of units a worker can produce in a day is 30. The learning curve for the number of units N produced per day after a new employee has worked days is modeled by After 20 days on the job, a worker is producing 19 units in a day. How many days should pass before this worker is producing 25 units per day? 
A) 
about 36 days. 
B) 
about 45 days. 
C) 
about 30 days. 
D) 
about 10 days. 
Ans: 
A 
123. 
Determine the principal P that must be invested at interest rate r compounded continuously, so that $1,000,000 will be available for retirement in years , . 
A) 
$49787.07 
B) 
$50787.07 
C) 
$49000.04 
D) 
$40000.06 
Ans: 
A 
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