Deck 13: Exponential Functions and Logarithmic Functions

Question 1

Solve the problem.
The amount of particulate matter left in solution during a filtering process decreases by the equation P(n) = where n is the number of filtering steps. Find the amounts left for n = 0 and n = 5. (Round to
The nearest whole number.)

A) 700; 22
B) 700; 88
C) 1400 ; 88
D) 700; 5600

Answer 1

B

Question 2

Graph.
f(x) = - 3

A)
B)
C)
D)

Answer 2

B

Question 3

Solve the problem.
A computer is purchased for $4500. Its value each year is about 77% of the value the preceding year. Its value, in dollars, after t years is given by the exponential function V(t) = Find the value of the computer after
6 years.

A) $556.08
B) $20,790.00
C) $937.90
D) $722.18

Answer 3

C

Question 4

Solve the problem.
Suppose that $40,000 is invested at 6% interest, compounded annually. Find a function A for the amount in the account after t years.

A)
B)
C)
D)

Question 5

Solve the problem.
The number of dislocated electric impulses per cubic inch in a transformer increases when lightning strikes by D(x) = where x is the time in milliseconds of the lightning strike. Find the number of dislocated
Impulses at x = 0 and x = 5 .

A) 2000 ; 32,000
B) 1000 ; 10,000
C) 1000 ; 32,000
D) 1000 ; 4000

Question 6

Graph.

A)
B)
C)
D)

Question 7

Solve the problem.
The half-life of a certain radioactive substance is 8 years. Suppose that at time t = 0, there are 29 g of the substance. Then after t years, the number of grams of the substance remaining will be:
N(t) = How many grams of the substance will remain after 56 years? Round to the nearest hundredth when necessary.

A) 0.64 g
B) 1.28 g
C) 0.32 g
D) 2.56 g

Question 8

Graph.
f(x) =

A)
B)
C)
D)

Question 9

Solve the problem.
An accountant tabulated a firm's profits for four recent years in the following table: The accountant then fit both a linear graph and an exponential curve (seen below) to the data, in order to estimate future profits. Use the exponential graph to estimate the profits in the year 2001.

A) About $750,000
B) About $300,000
C) About $1,300,000
D) About $1,000,000

Question 10

Solve the problem.
The half-life of Cesium 134m is 3.0 hours. If the formula P(t) = gives the percent (as a decimal) remaining after time t (in hours), sketch P versus t.

A)
B)
C)
D)

Question 11

Solve the problem.
The number of bacteria growing in an incubation culture increases with time according to B(x) = where x is time in days. Find the number of bacteria when x = 0 and x = 3 .

A) 19,600 ; 78,400
B) 9800 ; 58,800
C) 9800 ; 39,200
D) 9800 ; 78,400

Question 12

Graph.
f(x) =

A)
B)
C)
D)

Question 13

Solve the problem.
An accountant tabulated a firm's profits for four recent years in the following table: The accountant then fit both a linear graph and an exponential curve (seen below) to the data, in order to estimate future profits. Use the linear graph to estimate the profits in the year 2002.

A) About $800,000
B) About $500,000
C) About $1,000,000
D) About $900,000

Question 14

Graph.
f(x) = + 2

A)
B)
C)
D)

Question 15

Graph.
f(x) =

A)
B)
C)
D)

Question 16

Solve the problem.
An accountant tabulated a firm's profits for four recent years in the following table: The accountant then fit both a linear graph and an exponential curve (seen below) to the data, in order to estimate future profits. Use the exponential graph to estimate the profits in the year 2002.

A) About $1,000,000
B) About $1,700,000
C) About $1,300,000
D) About $750,000

Question 17

Graph.
x = 2y

A)
B)
C)
D)

Question 18

Graph.
f(x) =

A)
B)
C)
D)

Question 19

Graph.
f(x) =

A)
B)
C)
D)

Question 20

Solve the problem.
An accountant tabulated a firm's profits for four recent years in the following table: The accountant then fit both a linear graph and an exponential curve (seen below) to the data, in order to estimate future profits. Use the linear graph to estimate the profits in the year 2001.

A) About $500,000
B) About $700,000
C) About $800,000
D) About $900,000

Question 21

Find f(x) and g(x) such that h(x) =
h(x) =

A)
B)
C)
D)

Question 22

Find f(x) and g(x) such that h(x) =
h(x) =

A)
B)
C)
D)

Question 23

Find f(x) and g(x) such that h(x) =
h(x) =

A)
B)
C)
D)

Question 24

Find the requested composition of functions.
Given f(x) = - 3 and g(x) = find

A) - 3
B)
C)
D) 3

Question 25

Find the inverse of the relation.
{(-5, -4), (5, 4), (-3, 6), (3, -6)}

A) {(-4, -5), (4, 5), (6, 5), (-6, 3)}
B) {(-4, -5), (4, 5), (6, -3), (-6, 3)}
C) {(-4, -5), (-5, 5), (6, -3), (-6, 3)}

Question 26

Find the inverse of the relation.
{(-8, -7), (7, 8), (-4, -3), (4, 3)}

A) {(3, -4), (-4, 7), (-7, -8), (-3, 4)}
B) {(-7, -8), (8, 7), (-3, -4), (3, 4)}
C) {(3, -4), (8, 7), (-7, 7), (-3, 4)}

Question 27

Find f(x) and g(x) such that h(x) =
h(x) =

A)
B)
C)
D)

Question 28

Find the requested composition of functions.
Given f(x) = 7x + 8 and g(x) = 5x - 1, find

A) 35x + 39
B) 35x + 15
C) 35x + 1
D) 35x + 7

Question 29

Find the requested composition of functions.
Given f(x) = -5x + 2 and g(x) = 2x + 4, find

A) x + 8
B) -10x + 8
C) -10x + 22
D) x - 8

Question 30

Find f(x) and g(x) such that h(x) =
h(x) =

A)
B)
C)
D)

Question 31

Find the requested composition of functions.
Given f(x) = nd g(x) = x - 3, find

A)
B) - 3
C)
D)

Question 32

Find the inverse of the relation.
{(-16, 3), (5, -16), (-14, -12)}

A) {(-16, -16), (-16, 5), (-12, -14)}
B) {(3, -16), (-16, 5), (-12, -14)}
C) {(3, -16), (-14, 5), (-12, -16)}

Question 33

Find f(x) and g(x) such that h(x) =
h(x) =

A)
B)
C)
D)

Question 34

Find f(x) and g(x) such that h(x) =
h(x) =

A)
B)
C)
D)

Question 35

Find f(x) and g(x) such that h(x) =
h(x) = - 9

A)
B)
C)
D)

Question 36

Find the requested composition of functions.
Given f(x) = and g(x) = 7x + 10, find

A)
B) x + 20
C) 7x + 60
D) x

Question 37

Find the requested composition of functions.
Given f(x) = and g(x) = find

A)
B)
C)
D)

Question 38

Find f(x) and g(x) such that h(x) =
h(x) = 7

A)
B)
C)
D)

Question 39

Find the requested composition of functions.
Given f(x) = + 8 and g(x) = - 8, find

A)
B)
C)
D)

Question 40

Find the inverse of the relation.
{(6, 0), (-4, 1), (-6, 2), (-8, 3)}

A) {(1, 0), (3, -6), (6, -6), (1, 2)}
B) {(0, 6), (1, -4), (2, -6), (3, -8)}
C) {(1, 0), (0, -6), (6, -4), (1, 2)}

Question 41

Find an equation of the inverse of the relation.
y =

A)
B)
C)
D)

Question 42

Find an equation of the inverse of the relation.
y = 4 + 6x

A) y = 6 - 4x
B) y = 6 + 4x
C) x = 6 + 4y
D) x = 4 + 6y

Question 43

Determine whether the function is one-to-one.

-f(x) = - 2

Question 44

Graph the equation of the relation using a solid line, and then graph the inverse of the relation using a dashed line.
y =

A)
B)
C)
D)

Question 45

Graph the relation using solid circles and the inverse using open circles.
{(-3, -12), (-5, -11), (-7, -10), (-9, -9)}

A)
B)
C)
D)

Question 46

Determine whether the function is one-to-one.

-f(x) = + x

Question 47

Graph the relation using solid circles and the inverse using open circles.
{(-6, 7), (-7, 6), (-9, -4), (9, 4)}

A)
B)
C)
D)

Question 48

Determine whether the function is one-to-one.

-f(x) = - 6

Question 49

Graph the relation using solid circles and the inverse using open circles.
{(-9, 3), (9, -3), (-7, -1), (7, 1)}

A)
B)
C)
D)

Question 50

Find an equation of the inverse of the relation.
y = + 5x

A)
B)
C)
D)

Question 51

Determine whether the function is one-to-one.

-f(x) = - 6

Question 52

Determine whether the function is one-to-one.

-f(x) = + 8

Question 53

Determine whether the function is one-to-one.

-f(x) =

Question 54

Determine whether the function is one-to-one.

-f(x) = 6x - 6

Question 55

Graph the equation of the relation using a solid line, and then graph the inverse of the relation using a dashed line.
y = 2 + 3x

A)
B)
C)
D)

Question 56

Graph the equation of the relation using a solid line, and then graph the inverse of the relation using a dashed line.
y = 7x - 8

A)
B)
C)
D)

Question 57

Graph the relation using solid circles and the inverse using open circles.
{(-1, 16), (-7, -2), (5, -11)}

A)
B)
C)
D)

Question 58

Graph the equation of the relation using a solid line, and then graph the inverse of the relation using a dashed line.
y =

A)
B)
C)
D)

Question 59

Find an equation of the inverse of the relation.
y = 2x - 7

A) y = -2x + 7
B) y = -7x + 2
C) x = 2y - 7
D) x = -7y + 2

Question 60

Determine whether the function is one-to-one.

-f(x) = 64 -

Question 61

Graph the function as a solid curve and its inverse as a dashed curve.
f(x) =

A)
B)
C)
D)

Question 62

Solve the problem.
A size 12 dress in Country C is size 44 in Country D. A function that converts dress sizes in Country C to those in Country D is f(x) = x + 32. Find a formula for the inverse of the function described.

A)
B)
C)
D)

Question 63

Use composition to verify whether or not the inverse is correct.

-

Question 64

Use composition to verify whether or not the inverse is correct.

-

Question 65

Determine whether the function is one-to-one.

-f(x) =

Question 66

Determine whether the given function is one-to-one. If so, find a formula for the inverse.
f(x) =

A)
B)
C) Not a one-to-one function
D)

Question 67

Use composition to verify whether or not the inverse is correct.

-

Question 68

Determine whether the given function is one-to-one. If so, find a formula for the inverse.
f(x) =

A)
B)
C) Not a one-to-one function
D)

Question 69

Use composition to verify whether or not the inverse is correct.

-

Question 70

Determine whether the given function is one-to-one. If so, find a formula for the inverse.
f(x) =

A)
B)
C) Not a one-to-one function
D)

Question 71

Solve the problem.
A size -10 dress in Country C is size -10 in Country D. A function that converts dress sizes in Country C to those in Country D is f(x) = x - 20. Find a formula for the inverse of the function described.

A)
B)
C)
D)

Question 72

Determine whether the given function is one-to-one. If so, find a formula for the inverse.
f(x) =

A) Not a one-to-one function
B)
C)
D)

Question 73

Graph the function as a solid curve and its inverse as a dashed curve.
f(x) =

A)
B)
C)
D)

Question 74

Determine whether the given function is one-to-one. If so, find a formula for the inverse.
f(x) = 4x + 3

A)
B)
C)
D) Not a one-to-one function

Question 75

Use composition to verify whether or not the inverse is correct.

-

Question 76

Use composition to verify whether or not the inverse is correct.

-

Question 77

Determine whether the given function is one-to-one. If so, find a formula for the inverse.
f(x) =

A)
B)
C) Not a one-to-one function
D)

Question 78

Determine whether the given function is one-to-one. If so, find a formula for the inverse.
f(x) =

A)
B) Not a one-to-one function
C)
D)

Question 79

Use composition to verify whether or not the inverse is correct.

-

Question 80

Graph the function as a solid curve and its inverse as a dashed curve.
f(x) = 2x

A)
B)
C)
D)