Deck 9: Exponential and Logarithmic Functions

Question 1

Determine whether the function is a one-to-one function.

- $$y = - \frac { 3 } { 7 } x - 9$$

A)Yes
B)No

Answer 1

Yes

Question 2

Determine whether the function is a one-to-one function.

A)Yes
B)No

Answer 2

Yes

Question 3

For the given functions f and g , find the indicated value.

- $\begin{array} { l } f ( x ) = x ^ { 2 } - 2 x + 4 , \quad g ( x ) = x ^ { 2 } - 2 x - 5 \\( f \circ g ) ( - 4 )\end{array}$

A)309
B)732
C)750
D)327

Answer 3

327

Question 4

For the given functions f and g , find the indicated composition.

- $$\begin{array} { l } f ( x ) = \frac { x - 7 } { 10 } , \quad g ( x ) = 10 x + 7 \\( g \circ f ) ( x )\end{array}$$

A) $x - \frac { 7 } { 10 }$
B)10x + 63
C)x
D)x + 14

Question 5

For the given functions f and g , find the indicated composition.

- $$\begin{array} { l } f ( x ) = \sqrt { x + 2 } , x \geq - 2 , \quad g ( x ) = 8 x - 6 \\( f \circ g ) ( x )\end{array}$$

A) $2 \sqrt { 2 x - 1 } , x \geq \frac { 1 } { 2 }$
B) $2 \sqrt { 2 x + 1 } , x \geq - \frac { 1 } { 2 }$
C) $8 \sqrt { x - 4 } , x \geq 4$
D) $8 \sqrt { x + 2 } - 6 , x \geq - 2$

Question 6

Determine whether the function is a one-to-one function.

- $$y = x ^ { 2 } + 6$$

A)Yes
B)No

Question 7

Determine whether the function is a one-to-one function.

- $$y = - x ^ { 2 } + 3$$

A)Yes
B)No

Question 8

Determine whether the function is a one-to-one function.

- $$\{ ( - 5,2 ) , ( - 4,2 ) , ( - 3,6 ) , ( - 2 , - 6 ) \}$$

A)Yes
B)No

Question 9

For the given functions f and g , find the indicated value.

- $f ( x ) = x ^ { 2 } + 5 x , \quad g ( x ) = x + 4$
$( f \circ g ) ( 2 )$

A)66
B) $5 \sqrt { 3 }$
C)18
D)0

Question 10

For the given functions f and g , find the indicated composition.

- $$\begin{array} { l } f ( x ) = 3 x + 13 , \quad g ( x ) = 5 x - 1 \\( f \circ g ) ( x )\end{array}$$

A)15x + 12
B)15x + 10
C)15x + 16
D)15x + 64

Question 11

For the given functions f and g , find the indicated value.

- $f ( x ) = \sqrt { x + 2 } , \quad g ( x ) = 5 x$
$( f \circ g ) ( 1 )$

A) $\sqrt { 7 }$
B) $\sqrt { 15 }$
C) $5 \sqrt { 3 }$
D) $5 \sqrt { 15 }$

Question 12

For the given functions f and g , find the indicated value.

- $f ( x ) = x ^ { 2 } + 6 x , \quad g ( x ) = x + 2$
$( g \circ f ) ( 4 )$

A)42
B)44
C)240
D)72

Question 13

Determine whether the function is a one-to-one function.

- $$\{ ( 6 , - 7 ) , ( - 1 , - 6 ) , ( - 3 , - 5 ) , ( - 5 , - 4 ) \}$$

A)Yes
B)No

Question 14

For the given functions f and g , find the indicated composition.

- $$\begin{array} { l } f ( x ) = - 2 x + 3 , \quad g ( x ) = 6 x + 9 \\( g\circ f ) ( x )\end{array}$$

A)12x + 27
B)-12x - 9
C)-12x + 21
D)-12x + 27

Question 15

For the given functions f and g , find the indicated composition.

- $$\begin{array} { l } f ( x ) = \frac { 7 } { x - 5 } , \quad g ( x ) = \frac { 3 } { 4 x } \\( f \circ g ) ( x )\end{array}$$

A) $\frac { 28 x } { 3 - 20 x }$
B) $\frac { 28 x } { 3 + 20 x }$
C) $\frac { 3 x - 15 } { 28 x }$
D) $\frac { 7 x } { 3 - 20 x }$

Question 16

For the given functions f and g , find the indicated value.

- $$\begin{array} { l } f ( x ) = 2 x + 4 , \quad g ( x ) = 4 x ^ { 2 } + 1 \\( g \circ f ) ( 1 )\end{array}$$

A)145
B)101
C)16
D)14

Question 17

Determine whether the function is a one-to-one function.

A)Yes
B)No

Question 18

For the given functions f and g , find the indicated composition.

- $$\begin{array} { l } f ( x ) = 4 x ^ { 2 } + 3 x + 4 , \quad g ( x ) = 3 x - 6 \\( g \circ f ) ( x )\end{array}$$

A) $4 x ^ { 2 } + 9 x + 6$
B) $12 x ^ { 2 } + 9 x + 6$
C) $4 x ^ { 2 } + 3 x - 2$
D) $12 x ^ { 2 } + 9 x + 18$

Question 19

Determine whether the function is a one-to-one function.

A)Yes
B)No

Question 20

For the given functions f and g , find the indicated composition.

- $\begin{array} { l } f ( x ) = x ^ { 2 } + 6 , \quad g ( x ) = x ^ { 2 } - 6 \\( f \circ g ) ( x )\end{array}$

A) $x ^ { 4 } - 12 x ^ { 2 } + 42$
B) $x ^ { 4 } + 12 x ^ { 2 } + 30$
C) $x ^ { 4 } + 30$
D) $x ^ { 4 } + 42$

Question 21

Determine whether the given function is one-to-one. If it is one-to-one, find its inverse function.

- $$f ( x ) = 6 x ^ { 2 }$$

A) $f ^ { - 1 } ( x ) = \frac { 1 } { 6 x ^ { 2 } }$
B) $f ^ { - 1 } ( x ) = \frac { 6 } { x ^ { 2 } }$
C) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = 6 \sqrt { \mathrm { x } }$
D)not a one-to-one function

Question 22

Determine whether the function is a one-to-one function.

- $$y = ( x + 5 ) ^ { 3 }$$

A)Yes
B)No

Question 23

Determine whether the given function is one-to-one. If it is one-to-one, find its inverse function.

-f(x)= 3x + 4

A) $f ^ { - 1 } ( x ) = \frac { x + 4 } { 3 }$
B) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } - 4 } { 3 }$
C) $f ^ { - 1 } ( x ) = - \frac { x + 3 } { 4 }$
D)not a one-to-one function

Question 24

Determine whether the function is a one-to-one function.

- $$y = x ^ { 2 } + 7 , x \geq 0$$

A)Yes
B)No

Question 25

A one-to-one function f is given. $\text { Find } \mathrm { f } ^ { - 1 } ( \mathrm { x } )$ and graph fwith a solid line and $f ^ { - 1 } ( x )$ with a dotted line on the same axes.

- $f ( x ) = 4 x$

A) $f ^ { - 1 } ( x ) = \frac { x } { 4 }$

B) $f ^ { - 1 } ( x ) = - \frac { x } { 4 }$

C) $f ^ { - 1 } ( x ) = - \frac { x } { 4 }$

D) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } } { 4 }$

Question 26

Determine whether the function is a one-to-one function.

- $$y = | x + 3 |$$

A)Yes
B)No

Question 27

Determine whether the given function is one-to-one. If it is one-to-one, find its inverse function.

- $$f ( x ) = \frac { 2 } { x }$$

A) $f ^ { - 1 } ( x ) = \frac { x } { 2 }$
B) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 2 } { \mathrm { x } }$
C) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = - 2 \mathrm { x }$
D)not a one-to-one function

Question 28

Determine whether the function is a one-to-one function.

- $$y = x ^ { 2 } + 4 x + 11$$

A)Yes
B)No

Question 29

A one-to-one function f is given. $\text { Find } \mathrm { f } ^ { - 1 } ( \mathrm { x } )$ and graph fwith a solid line and $f ^ { - 1 } ( x )$ with a dotted line on the same axes.

- $f ( x ) = x ^ { 3 } + 1$

A) $f ^ { - 1 } ( x ) = - \sqrt [ 3 ] { x - 1 }$

B) $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x - 1 }$

C) $f ^ { - 1 } ( x ) = - x ^ { 3 } + 1$

D) $f ^ { - 1 } ( x ) = - x ^ { 3 } - 1$

Question 30

Determine whether the given function is one-to-one. If it is one-to-one, find its inverse function.

- $f ( x ) = \sqrt { x - 1 } , x \geq 1$

A) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \mathrm { x } ^ { 2 } - 1 , \mathrm { x } \geq 0$
B) $f ^ { - 1 } ( x ) = ( x - 1 ) ^ { 2 } , x \geq 1$
C) $f^{-1}(x)=x^{2}+1, x \geq 0$
D)not a one-to-one function

Question 31

A one-to-one function f is given. $\text { Find } \mathrm { f } ^ { - 1 } ( \mathrm { x } )$ and graph fwith a solid line and $f ^ { - 1 } ( x )$ with a dotted line on the same axes.

- $f ( x ) = \sqrt { x + 5 } , x \geq - 5$

A) $f ^ { - 1 } ( x ) = x ^ { 2 } + 5 , x \geq 0$

B) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \mathrm { x } ^ { 2 } - 5 , \mathrm { x } \geq 0$

C) $f ^ { - 1 } ( x ) = x ^ { 2 } + 5 , x \geq 0$

D) $f ^ { - 1 } ( x ) = - x ^ { 2 } + 5 , x \leq 0$

Question 32

Determine whether the given function is one-to-one. If it is one-to-one, find its inverse function.

- $f ( x ) = x ^ { 3 } + 6$

A) $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x } - 6$
B) $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x + 6 }$
C) $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x - 6 }$
D)not a one-to-one function

Question 33

Determine whether the given function is one-to-one. If it is one-to-one, find its inverse function.

- $f ( x ) = x ^ { 2 } - 7$

A) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \mathrm { x } ^ { 2 } + 7$
B) $f ^ { - 1 } ( x ) = x ^ { 2 } - 7$
C) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \mathrm { x } + 7$
D)not a one-to-one function

Question 34

Determine whether the given function is one-to-one. If it is one-to-one, find its inverse function.

-f(x)= 4x

A) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = - 4 \mathrm { x }$
B) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } } { 4 }$
C) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 4 } { \mathrm { x } }$
D)not a one-to-one function

Question 35

Determine whether the function is a one-to-one function.

- $$y = ( x + 5 ) ^ { 2 }$$

A)Yes
B)No

Question 36

Determine whether the function is a one-to-one function.

- $$y = \sqrt { x + 5 } , x \geq - 5$$

A)Yes
B)No

Question 37

For the given function, find the domain and range of both f(x)and ${ f } ^ { - 1 } ( \mathrm { x } ).$

-{(6, -12), (5, -11), (3, -10), (1, -9)}

A) f: domain: $\{ - 12 , - 11 , - 10 , - 9 \}$
$~~~~$ range: $\{ 6,5,3,1 \}$
$\mathrm { f } ^ { - 1 }$ : domain: $\{ 6,5,3,1 \}$
$~~~~$ range: $\{ - 12 , - 11 , - 10 , - 9 \}$
B) f: domain: $\{ 6,5,3,1 \}$
$~~~~$ range: $\{ - 12 , - 11 , - 10 , - 9 \}$
$\mathrm { f } ^ { - 1 }$ : domain: $\{ - 12 , - 11 , - 10 , - 9 \}$
$~~~~$ range: $\{ 6,5,3,1 \}$
C) f: domain: $\{ - 12 , - 11 , - 10 , - 9 \}$
$~~~~$ range: $\{ 6,5,3,1 \}$
$\mathrm { f } ^ { - 1 }$ : domain: $\{ - 12 , - 11 , - 10 , - 9 \}$
$~~~~$ range: $\{ 6,5,3,1 \}$
D) f: domain: $\{ 6,5,3,1 \}$
$~~~~$ range: $\{ - 12 , - 11 , - 10 , - 9 \}$
$\mathrm { f } ^ { - 1 }$ : domain: $\{ 6,5,3,1 \}$
$~~~~$ range: $\{ - 12 , - 11 , - 10 , - 9 \}$

Question 38

Determine whether the function is a one-to-one function.

- $$y = x ^ { 2 } + 10 x + 29 , x \geq - 5$$

A)Yes
B)No

Question 39

Determine whether the given function is one-to-one. If it is one-to-one, find its inverse function.

- $f ( x ) = x ^ { 2 } - 1 , x \geq 0$

A) $f ^ { - 1 } ( x ) = \sqrt { x } + 1 , x \geq 0$
B) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt { \mathrm { x } + 1 } , \mathrm { x } \geq - 1$
C) $f ^ { - 1 } ( x ) = \sqrt { x - 1 } , x \geq 1$
D)not a one-to-one function

Question 40

For the given function, find the domain and range of both f(x)and ${ f } ^ { - 1 } ( \mathrm { x } ).$

-

A) $\begin{array} { l } \mathrm { f } : \quad \text { domain: } \{ x \mid x \geq - 4 \} \\~~~~\text { range: } \{ \mathrm { y } \mid \mathrm { y } \geq 0 \} \\\mathrm { f } ^ { - 1 } : \text { domain: } \{ x \mid \mathrm { x } \geq - 4 \} \\~~~~\text { range: } \{ \mathrm { y } \mid \mathrm { y } \geq 0 \}\end{array}$
B) f: domain: $\{ x \mid x \geq - 4 \}$
$~~~~$ range: $\{ y \mid y \geq 0 \}$
$\mathrm { f } ^ { - 1 }$ : domain: $\{ \mathrm { x } \mid \mathrm { x } \geq 0 \}$
$~~~~$ range: $\{ y \mid y \geq - 4 \}$
C) f: domain: $\{ x \mid x \geq 0 \}$
$~~~~$ range: $\{ y \mid y \geq - 4 \}$
$\mathrm { f } ^ { - 1 }$ : domain: $\{ x \mid \mathrm { x } \geq - 4 \}$
$~~~~$ range: $\{ y \mid y \geq 0 \}$
D) f: domain: $\{ x \mid x \geq 0 \}$
$~~~~$ range: $\{ y \mid y \geq - 4 \}$
$\mathrm { f } ^ { - 1 }$ : domain: $\{ \mathrm { x } \mid \mathrm { x } \geq 0 \}$
$~~~~$ range: $\{ y \mid y \geq - 4 \}$

Question 41

Determine whether the given functions are inverses of each other.

- $$f ( x ) = \sqrt { x } , x \geq 0 , \quad g ( x ) = x ^ { 2 } , x \geq 0$$

A)Yes
B)No

Question 42

Determine whether the given functions are inverses of each other.

- $$f ( x ) = 7 x , \quad g ( x ) = \frac { 7 } { x }$$

A)Yes
B)No

Question 43

Graph the function.

- $f ( x ) = \left( \frac { 1 } { 4 } \right) ^ { - x }$

A)
B)
C)
D)

Question 44

Determine whether the given functions are inverses of each other.

- $$f ( x ) = \sqrt { x } , x \geq 0 , \quad g ( x ) = \frac { 1 } { \sqrt { x } } , x \geq 0$$

A)Yes
B)No

Question 45

Solve the problem.

-Four bacteria are placed in a petri dish. The population will triple every day. The formula for the number of bacteria in the dish on day t is $\mathrm { N } ( \mathrm { t } ) = 4 ( 2 ) ^ { \mathrm { t } }$ where t is the number of days after the four bacteria are placed in the dish. How many bacteria are in the dish
Eight days after the four bacteria are placed in the dish?

A)144
B)12
C)256
D)48

Question 46

Graph the function.

- $f ( x ) = 5 ^ { x - 1 }$

A)
B)
C)
D)

Question 47

Determine whether the given functions are inverses of each other.

- $$f ( x ) = \frac { x - 4 } { 4 } , \quad g ( x ) = 4 x + 4$$

A)Yes
B)No

Question 48

Graph the function.

- $f ( x ) = \left( \frac { 1 } { 4 } \right) ^ { x + 1 }$

A)
B)
C)
D)

Question 49

A one-to-one function f is given. $\text { Find } \mathrm { f } ^ { - 1 } ( \mathrm { x } )$ and graph fwith a solid line and $f ^ { - 1 } ( x )$ with a dotted line on the same axes.

- $f ( x ) = \frac { 4 } { x } , x \geq 0$

A) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 4 } { \mathrm { x } } , \mathrm { x } \leq 0$

B) $f ^ { - 1 } ( x ) = \frac { 4 } { x } , x \geq 0 ; f ( x ) = f ^ { - 1 } ( x )$

C) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = - \frac { 4 } { \mathrm { x } } , \mathrm { x } \geq 0$

D) $f ^ { - 1 } ( x ) = - \frac { 4 } { x } , x \leq 0$

Question 50

Determine whether the given functions are inverses of each other.

- $$f ( x ) = \sqrt [ 5 ] { x - 3 } , \quad g ( x ) = x ^ { 5 } + 3$$

A)Yes
B)No

Question 51

Graph the function.

- $f ( x ) = \left( \frac { 1 } { 4 } \right) ^ { x }$

A)
B)
C)
D)

Question 52

Solve the problem.
Austin invested $12,000 in an account at 8% compounded quarterly. Find the amount in Austin's account after a period of 4 years.

A)$16,150.42
B)$16,473.43
C)$4473.43
D)$16,325.87

Question 53

Graph the function.

- $f ( x ) = 3 ^ { - x }$

A)
B)
C)
D)

Question 54

Determine whether the given functions are inverses of each other.

- $$f ( x ) = 7 x , \quad g ( x ) = \frac { x } { 7 }$$

A)Yes
B)No

Question 55

Graph the function.

- $f ( x ) = 3 ^ { x }$

A)
B)
C)
D)

Question 56

Graph the function.

- $f ( x ) = 2 ^ { x } + 1$

A)
B)
C)
D)

Question 57

Determine whether the given functions are inverses of each other.

- $$f ( x ) = \frac { x + 7 } { 4 } , \quad g ( x ) = 4 x + 7$$

A)Yes
B)No

Question 58

Graph the function.

- $f ( x ) = 3 ^ { x + 1 }$

A)
B)
C)
D)

Question 59

Solve the problem.

-The amount of a radioactive substance present, in grams, at time t in months is given by the formula $y = 7000 ( 2 ) ^ { - 0.2 t }.$ Find the number Find the numberof grams present in 3 years. If necessary, round to three decimal places.

A)4.761
B)461.828
C)4618.278
D)47.608

Question 60

Determine whether the given functions are inverses of each other.

- $$f ( x ) = x ^ { 4 } - 19 , \quad g ( x ) = \sqrt [ 4 ] { x - 19 }$$

A)Yes
B)No

Question 61

Write the equation in logarithmic form.

- $2 ^ { - 2 } = \frac { 1 } { 4 }$

A) $\log _ { - 2 } \frac { 1 } { 4 } = 2$
B) $\log _ { 2 } \frac { 1 } { 4 } = - 2$
C) $\log _ { 1 / 4 } 2 = - 2$
D) $\log _ { 2 } - 2 = \frac { 1 } { 4 }$

Question 62

Write the equation in logarithmic form.

- $$\mathrm { a } ^ { \mathrm { b } } = \mathrm { q }$$

A)loga b = q
B)logq b = a
C)logq a = b
D)loga q = b

Question 63

Write the equation in logarithmic form.

- $343 ^ { 1 / 3 } = 7$

A) $\log _ { 343 } \frac { 1 } { 3 } = 7$
B) $\log _ { 7 } \frac { 1 } { 3 } = 343$
C) $\log _ { 343 } 7 = \frac { 1 } { 3 }$
D) $\log _ { 3 } 343 = 7$

Question 64

Write the equation in logarithmic form.

- $e ^ { - 1 / 2 } = 0.6065$

A) $- \frac { 1 } { 2 }$
B) $\log _e \left( - \frac { 1 } { 2 } \right) = 0.6065$
C) $\log _ { 0.6065 } \left( - \frac { 1 } { 2 } \right) = \mathrm { e }$
D) $\log _ { 0.6065 }e = - \frac { 1 } { 2 }$

Question 65

Write the equation in exponential form.

- $\log _ { 1 / 2 } \left( \frac { 1 } { 8 } \right) = 3$

A) $\left( \frac { 1 } { 2 } \right) ^ { 1 / 8 } = 3$
B) $\left( \frac { 1 } { 2 } \right) ^ { 3 } = \frac { 1 } { 8 }$
C) $\left( \frac { 1 } { 8 } \right) ^ { 3 } = \frac { 1 } { 2 }$
D) $3 ^ { 1 / 2 } = \frac { 1 } { 8 }$

Question 66

Write the equation in logarithmic form.

- $25 ^ { - 1 / 2 } = \frac { 1 } { 5 }$

A) $\log _ { - 1 / 2 } 25 = \frac { 1 } { 5 }$
B) $\log _ { 1 / 5 } 25 = - \frac { 1 } { 2 }$
C) $\log _ { 25 } \left( - \frac { 1 } { 2 } \right) = \frac { 1 } { 5 }$
D) $\log _ { 25 } \left( \frac { 1 } { 5 } \right) = - \frac { 1 } { 2 }$

Question 67

Write the equation in exponential form.

- $\log _ { 1 / 2 } 4 = - 2$

A) $( - 2 ) ^ { 1 / 2 } = 4$
B) $\left( \frac { 1 } { 2 } \right) ^ { - 2 } = 4$
C) $\left( \frac { 1 } { 2 } \right) ^ { 2 } = 4$
D) $4 ^ { 1 / 2 } = 2$

Question 68

Solve the problem.

-A sample of 1000 g of lead-210 decays to polonium-210 according to the function given by $\mathrm { A } ( \mathrm { t } ) = 1000 ( 2.718 ) ^ { - 0.032 t } ,$ where t is time in years. What is the amount of the sample, to the nearest gram, after 40 years?

A)3596 g
B)16 g
C)202 g
D)278 g

Question 69

Find the unknown value.

- $\log _ { 7 } \frac { 1 } { 343 } = y$

A)-49
B)49
C)3
D)-3

Question 70

Write the equation in logarithmic form.

- $$10 ^ { 0.6931 } = 2$$

A) $\log _ { 0.6931 } 10 = 2$
B) $\log _ { 10 } 2 = 0.6931$
C) $\log _ { 10 } 0.6931 = 2$
D) $\log_{ 0.6931}2 = 10$

Question 71

Write the equation in logarithmic form.

- $5 ^ { 2 } = 25$

A) $\log _ { 2 } 25 = 5$
B) $\log _ { 5 } 25 = 2$
C) $\log _ { 5 } 2 = 25$
D) $\log _ { 25 } 5 = 2$

Question 72

Find the unknown value.

- $\log _ { 5 } 625 = y$

A)20
B)5
C)4
D)625

Question 73

Solve the problem.

-The expected future population of a small town, which currently has 7900 residents, can be approximated by the formula $y = 7900 ( 1.8 ) ^ { - 0.2 t }$ where t is the number of years in the future. Find the expected population of the town 30 years in the future.

A)2844
B)7900
C)232
D)3

Question 74

Write the equation in exponential form.

- $\log _ { 4 } \left( \frac { 1 } { 16 } \right) = - 2$

A) $2 ^ { 4 } = \frac { 1 } { 16 }$
B) $4 ^ { 16 } = 2$
C) $\left( \frac { 1 } { 16 } \right) ^ { 2 } = 4$
D) $4 ^ { - 2 } = \frac { 1 } { 16 }$

Question 75

Write the equation in logarithmic form.

- $\left( \frac { 1 } { 5 } \right) ^ { 2 } = \frac { 1 } { 25 }$

A) $\log _ { 1 / 5 } \frac { 1 } { 25 } = 2$
B) $\log _ { 2 } \frac { 1 } { 25 } = \frac { 1 } { 5 }$
C) $\log _ { 1 / 25 } \frac { 1 } { 5 } = 2$
D) $\log _ { 1 / 5 } 2 = \frac { 1 } { 25 }$

Question 76

Write the equation in exponential form.

- $\log _ { 2 } 8 = 3$

A) $3 ^ { 2 } = 8$
B) $2 ^ { 3 } = 8$
C) $8 ^ { 3 } = 2$
D) $2 ^ { 8 } = 3$

Question 77

Solve the problem.
The function D(h)= 5(2.718)-0.4h can be used to determine the milligrams D of a certain drug in a patient's bloodstream h hours after the drug has been given. How many milligrams,rounded to two decimal places, will
Be present after 8 hours?

A)1.08 mg
B)122.62 mg
C)0.20 mg
D)3.49 mg

Question 78

Solve the problem.

-The value V of a car that is t years old can be modeled byed by $\mathrm { V } ( \mathrm { t } ) = 19,608 ( 0.83 ) ^ { \mathrm { t } }.$ . According to the model According to the mode, what is the value, to the nearest dollar, of a 3 year old car?

A)$4903
B)$13,508
C)$11,212
D)$48,824

Question 79

Find the unknown value.

- $\log _ { 9 } \frac { 1 } { 81 } = y$

A)-2
B)9
C)-9
D)2

Question 80

Write the equation in exponential form.

- $\log _ { 125 } 5 = \frac { 1 } { 3 }$

A) $125 ^ { 1 / 3 } = 5$
B) $5 ^ { 1 / 3 } = 125$
C) $5 ^ { 125 } = \frac { 1 } { 3 }$
D) $\left( \frac { 1 } { 3 } \right) ^ { 5 } = 125$