Deck 9: Exponential and Logarithmic Functions

Question 1

Write the logarithmic statement in exponential form. For example, "log ₂ 8 = 3" becomes "2 ³ = 8" in exponential form. log ₁₀ 100 = 2

A) 10 ² = -100
B) 10 ² = 0
C) 2 ¹⁰ = 100
D) 10 ² = 100
E) 10 ¹⁰⁰ = 2

Answer 1

10 ² = 100

Question 2

Graph the function.

A)
B)
C)
D)

Answer 2

Question 3

Graph the exponential function. f ( x ) = 3 ^x

A)
B)
C)
D)

Answer 3

Question 4

Graph the exponential function. f ( x ) = 3 ^{x + 2}

A)
B)
C)
D)

Question 5

Graph the function.

A)
B)
C)
D)
E) none of these

Question 6

The population of the earth is approximately 6 billion people and is growing at an annual growth rate of 1.9%. Assuming a Malthusian growth model, find the world population in 45 years. Round your answer to the nearest tenth.

A) 12.4 billion
B) 14.8 billion
C) 12.1 billion
D) 14.1 billion

Question 7

Graph the exponential function. f ( x ) = e ^x - 5

A)
B)
C)
D)

Question 8

Use the formula to find the total amount of money accumulated at the end of the indicated time period for the following investments. Please round the answers to the nearest hundredth. $300 for 13 years at 8% compounded semiannually.

A) $813.02
B) $830.96
C) $823.83
D) $831.74
E) $875.65

Question 9

An account now contains $11,000 and has been accumulating 7% annual interest, compounded continuously, for 10 years. Find the initial deposit.

A) $5,448.44
B) $5,462.44
C) $5,467.00
D) $5,463.69
E) $5,466.19

Question 10

Graph the exponential function . Graph the exponential function on the same axes in order to compare them.

A)
B)
C)
D)
E)

Question 11

Assuming a Malthusian growth model and annual growth rate of 1.9%, by what factor will the current population of the earth increase in 45 years?

A) 4.3
B) 2.9
C) 3.2
D) 4.2
E) 2.4

Question 12

Graph the exponential function . Graph the exponential function on the same axes in order to compare them.

A)
B)
C)
D)
E)

Question 13

Graph the exponential function.

A)
B)
C)
D)

Question 14

Use the formula to find the total amount of money accumulated at the end of the indicated time period by compounding continuously. Please round the answers to the nearest hundredth. $7,000 for 35 years at 13%.

A) $606,927.99
B) $529,502.67
C) $566,096.83
D) $466,849.94
E) $592,807.49

Question 15

Graph the exponential function.

A)
B)
C)
D)

Question 16

Write the logarithmic statement in exponential form. For example, "log ₂ 8 = 3" becomes "2 ³ = 8" in exponential form. log ₁₀ 0.1 = -1

A) 1 ^-10 = 0.1
B) 10 ^-1 = 0.1
C) 10 ¹ = 0.1
D) 10 ^-0.1 = 1
E) 10 ^0.1 = -1

Question 17

An initial deposit of $26,000 grows at an annual rate of 7% for 20 years. Compare the final balances resulting from continuous compounding and annual compounding. Round the answers to the nearest cent.

A) $100,610.89 from annual compounding; $105,433.70 from continuous compounding
B) $100,611.80 from annual compounding; $105,435.20 from continuous compounding
C) $100,613.85 from annual compounding; $105,455.20 from continuous compounding
D) $100,608.80 from annual compounding; $105,437.25 from continuous compounding

Question 18

An investment of $7,000 earns 6% interest, compounded continuously. What will the investment be worth in 8 years?

A) $11,293.52
B) $11,313.71
C) $11,309.36
D) $11,312.52
E) $11,301.86

Question 19

The radioactive material Iodine-131 decays according to the formula , where t is expressed in days. To the nearest hundredth, how much Iodine-131 will be left if a sample of 325 grams decays for 15 days?

A) 285.24 grams
B) 88.13 grams
C) 83.78 grams
D) 0 grams
E) None of these

Question 20

A 4 year certificate of deposit pays an annual rate of 8%, compounded daily. The maximum allowable deposit is $17,000. What is the most interest a depositor can earn from the CD? Round the result to the nearest cent.

A) $6,410.35
B) $6,510.45
C) $6,310.25
D) $6,400.34
E) $6,420.36

Question 21

Find the value, if possible. Give the answer to four decimal places.

A) 0.3471
B) 0.3411
C) 0.3642
D) 0.3586
E) none of these

Question 22

Find the value, if possible. Give the answer to four decimal places.

A) - 0.6330
B) - 0.6482
C) - 0.6675
D) - 0.5656
E) none of these

Question 23

Graph the function . Remember that the graph of is given.

A)
B)
C)
D)

Question 24

Use your calculator to find x when given ln x . Express answer to four decimal places.

A) 12.7894
B) 12.7294
C) 12.7694
D) 12.7394
E) 12.7594

Question 25

Graph by reflecting the graph of across the line y = x .

A)
B)
C)

Question 26

Use your calculator to find x when given ln x . Express answer to four decimal places.

A) 1.1838
B) 1.1238
C) 1.1638
D) 1.1338
E) 1.1538

Question 27

Assume that , , and . Use these values and the properties of logarithms to find the value. Do not use a calculator.

A) 3.1661
B) 2.2588
C) 1.3929
D) 2.1583
E) 2.5814

Question 28

Graph the function . Remember that the graph of is given.

A)
B)
C)

Question 29

Use a calculator to find each common logarithm. Express answer to four decimal places.

A) 3.5456
B) 3.4856
C) 3.4456
D) 3.5156
E) 3.5656

Question 30

An earthquake has a period of second, and an amplitude of micrometers. Find its measure on the Richter scale.

A)
B)
C)
D)
E)

Question 31

Which of these graphs could represent the graph of ?

A)
B)
C)
D)
E)

Question 32

Graph by graphing .

A)
B)
C)

Question 33

Calculate how many times more intense an earthquake with a Richter number of 8.1 is than an earthquake with a Richter number of 6.2. Please round the answer to the whole number.

A) 84
B) 87
C) 79
D) 89
E) 81

Question 34

Use your calculator to find x when given ln x . Express answer to four decimal places.

A) 0.0568
B) 0.0768
C) 0.1068
D) 0.0868
E) 0.0468

Question 35

Graph the function . Remember that the graph of is given.

A)
B)
C)
D)

Question 36

Find the value, if possible. Give the answer to four decimal places.

A) 3.2484
B) 3.3051
C) 3.2088
D) 3.2677
E) none of these

Question 37

Write the logarithmic statement in exponential form. For example, "log 2 8 = 3" becomes "2 ³ = 8" in exponential form.

A)
B)
C)
D)
E)

Question 38

How long will it take $1,500 to double itself if it is invested at 5% interest compounded semiannually? Please round the answer to the nearest tenth.

A) 14.0 years
B) 17.0 years
C) 14.5 years
D) 13.0 years
E) 15.0 years

Question 39

Use a calculator to find each common logarithm. Express answer to four decimal places.

A) 0.8579
B) 0.9579
C) 0.8779
D) 1.3579
E) 0.8279

Question 40

Which of these graphs could represent the graph of ?

A)
B)
C)
D)
E)

Question 41

Write the logarithm as a sum and/or difference of logarithms of a single quantity. Then simplify if possible. Assume that q and w are positive numbers.

A)
B)
C)
D)
E)

Question 42

Assume that , , , and are positive numbers.Use the properties of logarithms to write the expression in terms of the logarithms of x , y , and z .

A) log _b x log _b y log _b z
B) log _b x + log _b y + log _b z
C) - log _b x - log _b y - log _b z
D) log _b x - log _b y - log _b z

Question 43

A piece of machinery valued at $38,000 depreciates at a rate of 7% yearly. How long will it take until it has a value of $19,000? Please round the answer to the nearest tenth.

A) 11.9 years
B) 14.9 years
C) 12.9 years
D) 9.9 years
E) 8.9 years

Question 44

Use the change of base formula to identify the expression that is equivalent to .

A)
B)
C)
D)

Question 45

Use a calculator and the change-of-base formula to find the logarithm to four decimal places.

A) 1.0419
B) - 1.4650
C) 1.3645
D) - 1.4572
E) 2.2304

Question 46

How long will it take $200 to triple itself if it is invested at 8% interest compounded continuously? Please round the answer to the nearest tenth.

A) 12.7 years
B) 14.2 years
C) 16.7 years
D) 14.7 years
E) 13.7 years

Question 47

Assume that x , y , and b ( b ≠ 1) are positive numbers. Use the properties of logarithms to write the expression in terms of the logarithms of x and y .

A)
B)
C)
D)
E)

Question 48

Assume that , , , and are positive numbers. Use the properties of logarithms to write the expression in terms of the logarithms of , , and .

A)
B)
C)
D)
E)

Question 49

Assume that , , , and are positive numbers Use the properties of logarithms to write the expression in terms of the logarithms of , , and .

A)
B)
C)
D)
E)

Question 50

Use the properties of logarithms to write as the logarithm of a single quantity. Assume x and y are positive numbers.

A)
B)
C)
D)

Question 51

Assume that and . Use the change-of-base formula to find the logarithm to four decimal places.

A) 1.6812
B) 0.5579
C) 2.4771
D) 1.7925

Question 52

Find the value, if possible. Give the answer to four decimal places.

A) 0.3738
B) 0.3459
C) 0.3575
D) 0.3631
E) none of these

Question 53

Use the properties of logarithms to write as a sum, difference, or product of logarithms. Assume x and z are positive numbers.

A)
B)
C)
D)

Question 54

Write the logarithmic expression as one logarithm. Assume that u , i , and p are positive numbers.

A)
B)
C)
D)
E)

Question 55

Which of these graphs could represent the graph of y = ln 3 x ?

A)
B)
C)
D)

Question 56

Which of the following could represent the graph of y = 0.5ln x + 1?

A)
B)
C)
D)

Question 57

Assume that , and . Use these values and the properties of logarithms to find the value. Do not use a calculator.

A) 0.1383
B) 0.2466
C) 0.0807
D) 0.1461
E) 0.1230

Question 58

Assume that , , and . Use these values and the properties of logarithms to find the value. Do not use a calculator.

A) 1.4905
B) 2.3978
C) 3.2637
D) 2.4983
E) 2.9214

Question 59

How long will it take $900 to double itself if it is invested at 11% interest compounded semiannually? Please round the answer to the nearest tenth.

A) 6.5 years
B) 9.5 years
C) 7.0 years
D) 5.5 years
E) 7.5 years

Question 60

Assume that x and b ( b ≠ 1) are positive numbers. Use the properties of logarithms to write the expression as the logarithm of a single quantity.

A)
B)
C)
D)
E)

Question 61

Suppose that Nora invested $900 at 9.25% compounded annually for 9 years and Patti invested $900 at 9% compounded quarterly for 9 years. At the end of 9 years, who will have the most money and by how much (to the nearest dollar)?

A) Nora by $10
B) Patti by $3
C) Nora by $3
D) Patti by $10
E) They will have equal amounts of money.

Question 62

Calculate how many times more intense an earthquake with a Richter number of 8.1 is than an earthquake with a Richter number of 6.9. Please round the answer to the whole number.

A) 21
B) 24
C) 16
D) 26
E) 18

Question 63

How long will it take $800 to double itself if it is invested at 5% interest compounded semiannually? Please round the answer to the nearest tenth.

A) 14.0 years
B) 17.0 years
C) 14.5 years
D) 13.0 years
E) 15.0 years

Question 64

Solve the logarithmic equation. Check the solution.

A) x = 0
B) x = 1
C) x = 2
D) x = 3

Question 65

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 dollars, will depreciate to a value of V dollars in n years, where n is given by the formula: A computer that cost $14,000 has a life expectancy of 5 years. If it has depreciated to a value of $1,600, how old is it? Round the answer to the nearest tenth of the year.

A) 4.2 years old
B) 6.1 years old
C) 2.5 years old
D) 5.3 years old
E) 4.7 years old

Question 66

Solve the logarithmic equation. Check the solution.

A) 10
B) 1,000
C) 10,000
D) 100
E) 1

Question 67

Solve the exponential equation and express approximate solutions to the nearest hundredth. 7 ^x + 4 = 41

A) x = 1.81
B) x = 1.86
C) x = 2.07
D) x = 1.74
E) x = 2.01

Question 68

Solve the logarithmic equation. Check the solution.

A) x = 5
B) x = 4
C) x = 7
D) x = 6

Question 69

Solve the exponential equation and express approximate solutions to the nearest hundredth. 8 ^{25 x + 3} = 34 ^{x + 8}

A) x = 0.75
B) x = 0.83
C) x = 0.91
D) x = 0.45
E) x = 8.48

Question 70

Find the dB gain of an amplifier if the output voltage is 30 volts when the input voltage is 0.6 volt. Round your answer to the nearest hundredth.

A) 3.00 dB
B) 49.24 dB
C) 1.70 dB
D) 33.98 dB
E) None of these

Question 71

Solve the exponential equation and express solution to the nearest hundredth.

A) x = 1.76
B) x = 2.16
C) x = 1.26
D) x = 2.36
E) x = 1.96

Question 72

The number of grams Q of a certain radioactive substance present after t seconds is given by the equation . How many grams remain after 14 seconds? Please round the answers to the nearest whole.

A) Q = 1,309 grams
B) Q = 1,283 grams
C) Q = 1,490 grams
D) Q = 1,232 grams
E) Q = 1,233 grams