Deck 4: Exponential and Logarithmic Functions

Question 1

Graph using a table of values and integer inputs between -3 and 3. Indicate whether the function is increasing or decreasing.
y =

Answer 1

decreasing (Gridlines are spaced one unit apart.)

Question 2

Use the following to answer questions :
Use a calculator (as needed) to evaluate the function as indicated. Round values to the thousandths place if necessary.
P(t) = 1700
t = 8.5

Answer 2

0.008

Question 3

Use the following to answer questions :
Use a calculator (as needed) to evaluate the function as indicated. Round values to the thousandths place if necessary.
P(t) = 1700
t = 7

A) 99.473
B) 103.724
C) 107.618
D) 111.831

Answer 3

99.473

Question 4

Determine a likely candidate for the inverse function by reasoning and test points.
f(x) = x + 3

Question 5

Compute . f(x) =

A) f ^-1(x) = x³ - 5
B) f ^-1(x) = x³ + 5
C) f ^-1(x) = (x + 5)³
D) f ^-1(x) =

Question 6

Graph using a table of values and integer inputs between -3 and 3. y = 5^x

A)

(Gridlines are spaced one unit apart.)
B)

(Gridlines are spaced one unit apart.)
C)

(Gridlines are spaced one unit apart.)
D)

(Gridlines are spaced one unit apart.)

Question 7

Determine whether the function is one-to-one. If not, state why.
{(3, 4), (1, 7), (8, 3), (-1, 4), (2, 5), (6, -1)}

Question 8

Use the following to answer questions :
Use a calculator (as needed) to evaluate the function as indicated. Round values to the thousandths place if necessary.
P(t) = 5800 · 16^x
t =

A) 548,013.289
B) 548,025.391
C) 548,036.523
D) 548,048.647

Question 9

Prove (using compositions) that g(x) = f ^-1(x).
f(x) = -3x + 1, g(x) =

Question 10

Compute . f(x) = x³ + 8

A) , x ≥ 0
B)
C) , x ≥ 8
D)

Question 11

Use the following to answer questions :
Use a calculator (as needed) to evaluate the function as indicated. Round values to the thousandths place if necessary.
P(t) = 5800 · 16^x
t =

Question 12

Determine whether the graph is that of a one-to-one function. If not, give an example of how the definition of one-to-oneness is violated. (Gridlines are spaced one unit apart.)

Question 13

Plot f(x) and its inverse f ^-1(x) on the same grid and "dash-in" the line y = x.
f(x) = 2x + 3; f ^-1(x) =

Question 14

Determine whether the function is one-to-one. If not, state why.
{(-2, 5), (-4, 8), (3, 4), (-6, 7), (-3, 6), (1, 0)}

Question 15

Determine if the function is one-to-one by noting the functions family to which it belongs and mentally picturing the shape of its graph. f(x) = 4x - 10

A) one-to-one
B) not one-to-one

Question 16

Determine if the function is one-to-one by noting the functions family to which it belongs and mentally picturing the shape of its graph. f(x) = 8x² + 5

A) one-to-one
B) not one-to-one

Question 17

Determine if the function is one-to-one by noting the functions family to which it belongs and mentally picturing the shape of its graph. f(x) = -|x + 7|-5

A) one-to-one
B) not one-to-one

Question 18

Find the inverse function of the one-to-one function given.
{(-1, 1), (-3, 4), (4, 0), (-5, 3), (-2, 2)}

Question 19

Plot f(x) and its inverse f ^-1(x) on the same grid and "dash-in" the line y = x.
f(x) = (x + 3)², x ≥ -3; f ^-1(x) =

Question 20

Compute . f(x) = 2x - 6

A)
B)
C)
D)

Question 21

Graph by the following function by translating the basic function y = b^x, sketching the asymptote, and strategically plotting a few points to round out the graph.
y =

Question 22

Graph by the following function by translating the basic function y = b^x, sketching the asymptote, and strategically plotting a few points to round out the graph. y =

A)

(Gridlines are spaced one unit apart.)
B)

(Gridlines are spaced one unit apart.)
C)

(Gridlines are spaced one unit apart.)
D)

(Gridlines are spaced one unit apart.)

Question 23

Graph by the following function by translating the basic function y = b^x, sketching the asymptote, and strategically plotting a few points to round out the graph. Clearly state what shifts are applied.
y = 2^{x + 1} - 2

Question 24

Graph by the following function by translating the basic function y = b^x, sketching the asymptote, and strategically plotting a few points to round out the graph. y =

A)

(Gridlines are spaced one unit apart.)
B)

(Gridlines are spaced one unit apart.)
C)

(Gridlines are spaced one unit apart.)
D)

(Gridlines are spaced one unit apart.)

Question 25

Graph by the following function by translating the basic function y = b^x, sketching the asymptote, and strategically plotting a few points to round out the graph. y = 2^{x - 1}

A)

(Gridlines are spaced one unit apart.)
B)

(Gridlines are spaced one unit apart.)
C)

(Gridlines are spaced one unit apart.)
D)

(Gridlines are spaced one unit apart.)

Question 26

Write the equation in exponential form.
2 = log ₅ 25

Question 27

Solve the exponential equation. 27^{x + 2} = 3

A)
B)
C)
D)

Question 28

Determine the value of the expression without using a calculator. log ₃ 9

A)
B)
C) 2
D) -2

Question 29

Graph by the following function by translating the basic function y = b^x, sketching the asymptote, and strategically plotting a few points to round out the graph.
y =

Question 30

Determine the value of x by writing the equation in exponential form. log _x

= -4

A) 3
B) -3
C)
D)

Question 31

$200 is invested in an account paying 7.5% compounded annually. How much will the account be worth after 8 years? [Round to the nearest cent. Use the compound interest formula .]

A) $\approx$ $351.54
B) $\approx$ $353.38
C) $\approx$ $356.70
D) $\approx$ $361.98

Question 32

Determine the value without using a calculator. log ₃

A)
B)
C) 2
D) -2

Question 33

Solve the exponential equation.
100^{x - 3} = 1000^x

Question 34

Graph by the following function by translating the basic function y = b^x, sketching the asymptote, and strategically plotting a few points to round out the graph. Clearly state what shifts are applied.
y = 4^-x

Question 35

Graph by the following function by translating the basic function y = b^x, sketching the asymptote, and strategically plotting a few points to round out the graph. Clearly state what shifts are applied.
y = 2^x + 2

Question 36

Determine the value without using a calculator.
log ₁₇ 17

Question 37

Solve the exponential equation. = 343

Question 38

Solve the exponential equation and check your answer by substituting into the original equation.
2^x = 8

Question 39

Write the equation in logarithmic form. 2⁴ = 16

A) 16 = log ₂ 4
B) 4 = log ₂ 16
C) 2 = log ₄ 16
D) 16 = log ₄ 2

Question 40

Determine the value of x by writing the equation in exponential form.
log ₂ x = 5

Question 41

Graph the exponential function. f(x) = e^{-x - 2} + 1

A)

(Gridlines are spaced one unit apart.)
B)

(Gridlines are spaced one unit apart.)
C)

(Gridlines are spaced one unit apart.)
D)

(Gridlines are spaced one unit apart.)

Question 42

Solve the equation by writing it in logarithmic form. Answer in exact form.

A) x =
B) x =
C) x =
D) x =

Question 43

Determine the domain of the function.

A) x $\in$ (-4, 2)
B) x $\in$ [-4, 2)
C) x $\in$ (-?, -4) $\cup$ (2, ?)
D) x $\in$ (-?, -4] $\cup$ (2, ?)

Question 44

Evaluate the expression using the change-of-base formula and either base 10 or base e. Answer in approximate form using 8 decimal places. log ₃ 27

A) 2.84767879
B) 2.98768768
C) 3.00000000
D) 3.32345613

Question 45

Use a calculator to evaluate ln 401, rounded to six decimal places.

A) 4.992827
B) 5.993961
C) 7.117417
D) 8.184048

Question 46

Use the following to answer questions :
The magnitude of an earthquake is given by the equation where I is the actual intensity of the earthquake and I₀ is the reference intensity (the smallest earth movement that can be recorded on a seismograph).
Find the intensity I of the earthquake given M(I) = 4.5. Round your answer to the nearest tenth.

A) ≈ 31,632.9I₀
B) ≈ 31,622.8I₀
C) ≈ 31,617.6I₀
D) ≈ 31,610.5I₀

Question 47

Graph the logarithmic function.
f(x) = -ln(x + 1)

Question 48

Solve the equation by writing it in exponential form. Answer in exact form and approximate form using a calculator (round to thousandths).
ln x = 1.587

Question 49

Use a calculator to find an approximate value, rounded to four decimal places. log 0.078

A) $\approx$ -1.7313
B) $\approx$ -1.4066
C) $\approx$ -1.1079
D) $\approx$ -0.1667

Question 50

Graph the function using transformations of y = log _b x and strategically plotting a few points.
f(x) = -log ₃(x + 2)

Question 51

Use the following to answer questions :
The magnitude of an earthquake is given by the equation where I is the actual intensity of the earthquake and I₀ is the reference intensity (the smallest earth movement that can be recorded on a seismograph).

-Find the value of M(I) when I = 81,500I₀. Round your answer to the nearest tenth.

A) $\approx$ 4.6
B) $\approx$ 4.7
C) $\approx$ 4.8
D) $\approx$ 4.9

Question 52

Solve the equation by writing it in exponential form. Answer in decimal form to the thousandths place. ln e^6x = -32.4

A) x = 0.027
B) x = 1.686
C) x = -0.644
D) x = -5.400

Question 53

Determine the domain of the function.

Question 54

Graph the logarithmic function. f(x) = ln(x - 2) + 3

A)

(Gridlines are spaced one unit apart.)
B)

(Gridlines are spaced one unit apart.)
C)

(Gridlines are spaced one unit apart.)
D)

(Gridlines are spaced one unit apart.)

Question 55

Graph the function using transformations of y = log _b x and strategically plotting a few points.
f(x) = log ₃ x + 2

Question 56

Determine the value of x by writing the equation in exponential form. log ₁₆ 32 = x

A)
B)
C) 2
D)

Question 57

Use a calculator to find an approximate value, rounded to four decimal places. log 732

A) $\approx$ 2.7411
B) $\approx$ 2.8645
C) $\approx$ 3.2966
D) $\approx$ 3.8057

Question 58

The time required for a population to triple is given by , where r represents the growth rate (expressed as a decimal) and T(r) gives the years required. How long would it take a population to triple if the growth rate were 3.9%? Round your answer to the nearest tenth.

A). $\approx$ 28.2 years
B). $\approx$ 28.3 years
C). $\approx$ 28.4 years
D). $\approx$ 28.5 years

Question 59

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

Question 60

Use a calculator to evaluate e^3.4, rounded to six decimal places.

A) 26.962966
B) 27.055977
C) 28.840644
D) 29.964100

Question 61

Use the properties of logarithms to write the expression as a sum or difference of simple logarithmic terms.

A)
B)
C)
D)

Question 62

Use the properties of logarithms to write the expression as a sum or difference of simple logarithmic terms.

Question 63

Solve using the method of your choice. Answer in approximate form rounded to four decimal places. 10^x = 29

A) x $\approx$ 1.4624
B) x $\approx$ 2.9000
C) x $\approx$ 3.3673
D) x $\approx$ 0.3367

Question 64

Solve using any appropriate method. Answer in exact form. ln(x + 1) + ln 8 = 6

A) x = e⁶ - 9
B) x = ln 6 - 9
C) x =
D) x =

Question 65

Solve using any appropriate method. Clearly identify any extraneous roots. If there are no solutions, so state. log(x + 20) - log x = log(x + 2)

A) x = -5, 4
B) x = 4, -5 is extraneous
C) x = 5, 4 is extraneous
D) No solution

Question 66

Use the properties of logarithms to write the expression as a single term. ln(x + 3) - ln(x + 1)

A)
B) ln(3)
C) ln[(x + 3)(x + 1)]
D) ln(2)

Question 67

Write the equation in the simplified form b^x = k (exponential term = constant). Do not solve. 4^x (4^{7x - 1}) = 16

A) 4^{6x - 1} = 16
B) 4^{8x - 1} = 16
C)
D)

Question 68

Solve using the method of your choice. Answer in exact form. 3^x = 2^{3x - 8}

A) x =
B) x =
C) x =
D) x =

Question 69

Solve using any appropriate method. Clearly identify any extraneous roots. If there are no solutions, so state. log(-x - 2) = log(3x) - log x

A) x = 0, -5
B) x = 0, 5
C) x = 5
D) No solution

Question 70

Solve the equation using the uniqueness property of logarithms.
log(10x + 10) = log 20

Question 71

Solve by converting to exponential form. log(3x - 5) = 2

A) x =
B) x =
C) x = 35
D) x = 34

Question 72

Write the equation in the simplified form b^x = k (exponential term = constant). Do not solve.
1 - 4e^0.2x = -35

Question 73

Solve the equation in two ways: by equating bases and using the uniqueness properties and by applying a base-10 or base-e logarithm and using the power property of logarithms.

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

Question 74

Write the equation in the simplified form log _b x = k (logarithmic term = constant). Do not solve. ln(x - 3) - ln x = -ln(5x)

A)
B) ln(5x³ - 15x²) = 0
C)
D) ln(5x - 15) = 0

Question 75

Use the properties of logarithms to write the expression as a single term.
ln(x + 7) + ln(7x)

Question 76

Solve using the method of your choice. Answer in exact form and approximate form rounded to four decimal places.
8^{x + 3} = 4602

Question 77

Use the power property of logarithms to rewrite the term as a product of a constant and a logarithmic term.
ln7^{4x - 3}

Question 78

Write the equation in the simplified form log _b x = k (logarithmic term = constant). Do not solve.
5log ₃ x + log ₃(x + 8) = -3

Question 79

Solve the equation in two ways: by equating bases and using the uniqueness properties and by applying a base-10 or base-e logarithm and using the power property of logarithms.
3^x = 27

Question 80

Compute the average rate of change of y = ln x over the interval [2, 2.0001]. Round your answer to the nearest hundredth

A) $\approx$ 0.49
B) $\approx$ 0.50
C) $\approx$ 0.62
D) $\approx$ 0.81