Free Printable Exponential & Logarithmic Quest Practice Problems

1.

log₃81

a)

2

b)

3

c)

4

d)

5

2.

log₅25

a)

2

b)

5

c)

125

3.

log₄16

a)

2

b)

4

c)

1/2

d)

-2

4.

log₄1

a)

0

b)

1

c)

4

d)

DNE

5.

a)

1/2

b)

√2

c)

2

d)

-2

6.

log₆6

a)

-1

b)

0

c)

2

d)

1

7.

log₂32

a)

5

b)

4

c)

16

d)

6

8.

log₈1

a)

0

b)

1

c)

2

d)

8

9.

log₅125

a)

0

b)

1

c)

2

d)

3

10.

log₇49

a)

0

b)

1

c)

2

d)

3

11.

log₆216

a)

0

b)

1

c)

2

d)

3

12.

log₃ $\frac{1}{27}$

a)

0

b)

-1

c)

-3

d)

3

13.

log₂ $\frac{1}{32}$

a)

5

b)

-5

c)

6

d)

-6

14.

log 10

a)

0

b)

1

c)

-1

d)

2

15.

log 100

a)

0

b)

1

c)

-2

d)

2

16.

log₃81 =

a)

2

b)

3

c)

4

d)

5

17.

log₅25 = ?

a)

2

b)

5

c)

125

18.

True or False: log₈64=2

a)

True

b)

False

19.

log₄1 =

a)

0

b)

1

c)

4

d)

DNE

20.

a)

100

b)

2

c)

10

d)

1

21.

a)

2

b)

-2

c)

-1/2

d)

1/2

22.

a)

1/2

b)

√2

c)

2

d)

-2

23.

a)

0

b)

1

c)

8

d)

1/8

24.

log₆6

a)

-1

b)

0

c)

2

d)

1

25.

log₂32

a)

5

b)

4

c)

16

d)

6

26.

a)

-3

b)

1/3

c)

3

d)

-25

27.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

28.

Rewrite log_pt = m in exponential form.

a)

p^t = m

b)

t^m = p

c)

m^t = p

d)

p^m = t

29.

Evaluate Log $\frac{1}{100}$

a)

2

b)

3

c)

$\frac{1}{10}$

d)

-2

30.

Evaluate $\log_3\ \left(\frac{1}{3}\right)$

a)

1

b)

-1

c)

$\frac{1}{3}$

d)

3.33

31.

Rewrite log_x95 = 2.3

a)

x^2.3 = 95

b)

95^2.3 = x

c)

2.3⁹⁵ = x

d)

x⁹⁵= 2.3

32.

Rewrite 1.6^(x+2) = 14.1

a)

log_1.614.1 = x+2

b)

log_1.6(x+2) = 14.1

c)

log_14.1(x+2) = 1.6

d)

log_(x+2)1.6 = 14.1

33.

Without a calculator, evaluate log₄1

a)

¹/₄

b)

0

c)

-1

d)

not possible

34.

List the following in order, least to greatest:

A) log₅ 30

B) log_0.25 32

C) log₇ 49

D) log₈ 40

a)

A,B,C,D

b)

A,B,D,C

c)

B,D,C,A

d)

B,D,A,C

35.

Evaluate log₁₂₅ 25

a)

²/₃

b)

³/₂

c)

¹/₆

d)

¹/₅

36.

$Evaluate\ \log_28$

(a)

37.

$Evaluate\ \log_864$

(a)

38.

$Evaluate\ \log_77$

(a)

39.

$Evaluate\ \log_381$

(a)

40.

$Evaluate\ \log_{10}1000$

(a)

41.

$Evaluate\ \log_61$

(a)

42.

$Evaluate\ \log_8\frac{1}{8}$

(a)

43.

$Evaluate\ \log_7\frac{1}{49}$

(a)

44.

$Evaluate\ \log_5\sqrt{5}$

(a)

45.

$Evaluate\ \log_93$

(a)

46.

log_x1000=3

a)

1

b)

10

c)

30

d)

3

47.

log₈(4x+4)=2

a)

15

b)

12

c)

10

d)

3

48.

log₆(2x + 3) = 3

a)

x = 106.5

b)

x = 100

c)

x = 16

d)

x = 50

49.

What is the range for
f(x)=-(1/3)^x+4?

a)

(0,∞)

b)

(-4,∞)

c)

(-∞, 0)

d)

(-∞,-4)

50.

What is the range for
f(x)=5^x-6-3?

a)

(3,∞)

b)

(-3,∞)

c)

(-∞, 3)

d)

(-∞, -3)

51.

What is the horizontal asymptote for the graph of
f(x)=13(0.5)^x-6?

a)

y=0.5

b)

y=13

c)

y=6

d)

y=0

52.

What is the horizontal asymptote for the graph of
f(x)=-2(3)^x+4-8 ?

a)

y=8

b)

y=-8

c)

x=-8

d)

x=-4

53.

Classify
f(x)=-19^-x

a)

Exponential Growth

b)

Exponential Decay

54.

Classify
f(x)=4/5(.8)^x-9

a)

Exponential Growth

b)

Exponential Decay

55.

Classify
f(x)=-3(1.75)^x-4+6

a)

Exponential Growth

b)

Exponential Decay

56.

What is the equation that best represents the graph?

a)

y=2^y

b)

y=2^x

c)

y=2^-x

d)

y=x²

57.

Is the pictured graph exponential growth, exponential decay, or linear or none?

a)

Exponential Growth

b)

Exponential Decay

c)

Linear

d)

None

58.

Given y=3^xdetermine the y-intercept

a)

(0,1)

b)

(0,3)

c)

No Y-intercept

d)

y=1

59.

Which of the following is an increasing exponential function whose y-intercept is 50?

a)

y = 50(.05)^x

b)

y = 50x - 4

c)

y = (2)^x + 50

d)

y = 50(1.4)^x

60.

Which is the best graph for $f\left(x\right)=2\left(3^x\right)$ ?

a)

b)

c)

d)

61.

Which graph represents $y=\frac{1}{2}\cdot4^x$

a)

b)

c)

d)

62.

Does the function represent exponential growth or decay?

y=\frac{1}{8}\left(5\right)^x

a)

Decay

b)

Growth

63.

Identify the y-intercept of the graph of the exponential function:

y=3\left(\frac{1}{2}\right)^x

a)

(3,0)

b)

(1/2, 0)

c)

(0,0)

d)

(0,3)

64.

What is the intercept of the exponential function?

a)

$\left(0,\ 3\right)$

b)

$\left(3,\ 0\right)$

c)

$\left(6,\ 0\right)$

d)

$\left(0,\ 6\right)$

65.

What function is present?

a)

Absolute Value

b)

Exponential Decay

c)

Linear Equation

d)

Exponential Growth

66.

What is the y-intercept of the function?

a)

2

b)

3

c)

1

d)

-2

67.

Which definition defines growth?

a)

B is greater than 1

b)

B is less then 1

c)

B is less than 0

d)

B is in greater than 0 but less than 1

68.

Which definition defines decay

a)

B is less then 1

b)

B is greater than 1

c)

B is greater then 0 but less then 1

d)

B is less then 0

69.

Growth or Decay?

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

a)

Growth

b)

Decay

70.

In the following decreasing exponential graph

a)

the base is greater than one

b)

the base is between 0 and 1

c)

the base is zero

d)

the base is a negative value

71.

Identify the y-intercept (initial value) in the function f(x)=13(.27)^x

a)

(.27)^x

b)

.27

c)

13

d)

3.51

72.

This is the horizontal line which the values of the function cannot fall below :

a)

Asymptote

b)

Growth Factor

c)

Axis of symmetry

d)

Curve

73.

Which graph represents $y=\frac{1}{2}\cdot4^x$

a)

b)

c)

d)

74.

Which is the best graph for $f\left(x\right)=-3^x$ ?

a)

b)

c)

d)

75.

Which is the best graph for $f\left(x\right)=2\left(3^x\right)$ ?

a)

b)

c)

d)

76.

Given y=3^xdetermine the y-intercept

a)

(0,1)

b)

(0,3)

77.

Using the parent function y=3^x what would the graph of y=3^x+1 look like?

a)

Horizontal Shift to the right 1 unit

b)

Horizontal shift to the left one unit

c)

Vertical shift one unit up

d)

Vertical shift one unit down

78.

What is the domain and range of the function y=2^x?
Use the graph to help!

a)

Domain: All Real Numbers
Range: y>0

b)

Domain: All Real Numbers
Range: y>1

c)

Domain: −2<x<∞
Range: y>0

d)

Domain: −∞<x<∞
Range: y>0

79.

What is the equation of the asymptote?

a)

x = -3

b)

x=5

c)

y= -3

d)

y=5

80.

Logarithmic functions are the inverse of...

a)

Linear Functions

b)

Exponential Functions

c)

Quadratic Functions

d)

Polynomial Functions

81.

Match the graph with its equation

a)

y = log₆(-x) + 1

b)

y = log₆(x − 2) + 1

c)

y = log₆(x + 2) - 1

d)

y = log(x-8) + 1

82.

Match the graph with its equation

a)

y = log₅ (x + 1) + 1

b)

y = log₅ (x - 1) + 1

c)

y = log₅ (x²) + 1

d)

y = log₅ (x)-1

83.

Select all the transformations that apply.

y = -2 log _1/2x

a)

Vertical stretch by 2

b)

Vertical shrink by 1/2

c)

Reflection across the y-axis

d)

Reflection across the x-axis

84.

Find the corresponding graph of
$-\log_4\left(x+1\right)+2$

a)

b)

c)

d)

85.

What is the domain and range of this graph?

a)

D: all real numbers
R: all real numbers

b)

D: all real numbers
R: y ≥ 0

c)

D: x ≥ 2
R: y ≥ 3

d)

D: x ≤ 2
R: y ≤ 3

86.

Which equation is the inverse of the equation above?

a)

b)

c)

d)

87.

Which graph best represents the following logarithmic function?
$y=\log_4x$

a)

b)

c)

d)

88.

Which graph best represents the following logarithmic function?
$y=\log_2x$

a)

b)

c)

d)

89.

Logarithmic functions are the inverse of...

a)

Linear Functions

b)

Exponential Functions

c)

Quadratic Functions

d)

Polynomial Functions

90.

Which graph best represents the following logarithmic function?
$y=\log_4x$

a)

b)

c)

d)

91.

Which graph best represents the following logarithmic function?
$y=\log_2x$

a)

b)

c)

d)

92.

Which function has a horizontal asymptote?

a)

exponential

b)

logarithm

c)

both

d)

neither

93.

Which function has a vertical asymptote?

a)

exponential

b)

logarithm

c)

both

d)

neither

94.

How are exponentials and logarithms related?

a)

They're cousins

b)

They're inverses

c)

They're not related

d)

They're reciprocals

95.

Classify the following graph.

a)

Exponential Growth

b)

Exponential Decay

c)

Logarithmic

d)

Rational

96.

Where is the asymptote?

a)

x = 1

b)

y = 1

c)

x = -1

d)

y = -1

97.

What is the domain?

a)

(-∞, ∞)

b)

(0, ∞)

c)

[1, ∞)

d)

(1, ∞)

98.

What is the range?

a)

(-∞, ∞)

b)

(0, ∞)

c)

[1, ∞)

d)

(1, ∞)

99.

What is the base?

a)

1

b)

5

c)

10

d)

3

100.

What is the domain of log(x)?

a)

(-∞, ∞)

b)

[0, ∞)

c)

(0, ∞)

d)

(∞, -∞)

101.

What is the range of log(x)?

a)

(-2, 4)

b)

(-∞, ∞)

c)

(-∞, 0)

d)

(∞, -∞)

102.

What is the x-intercept of log₇(x)?

a)

(2, 0)

b)

(-1, 0)

c)

(0, 1)

d)

(1, 0)

103.

When creating a graph for f(x)=log₇(x), what should be typed into the graphing calculator?

a)

y₁= log(7)x

b)

y₁= log(7x)

c)

y₁= log(x) / log(7)

d)

y₁= log(7) / log(x)

104.

Logarithmic functions are the inverse of...

a)

Linear Functions

b)

Exponential Functions

c)

Quadratic Functions

d)

Polynomial Functions

105.

Rewrite in log form: $6^3=216$

a)

$\log_3216=6$

b)

$\log_{216}6=3$

c)

$\log_63=216$

d)

$\log_6216=3$

106.

Rewrite in exponential form: $\log_525=2$

a)

$2^5=25$

b)

$5^{25}=2$

c)

$5^2=25$

d)

$25^2=5$

107.

Which the following graphs shows an exponential decay equation?

a)

b)

c)

d)

108.

Is the pictured graph growth, decay, or linear or none?

a)

Growth

b)

Decay

c)

Linear

d)

None

109.

Which function best describes the following graph?

a)

Logarithmic

b)

Exponential

110.

Rewrite in log form: $2^5=32$

a)

$\log_232=5$

b)

$\log_25=32$

c)

$\log_532=2$

d)

$\log_{32}5=2$

111.

Rewrite in exponential form: $\log_{23}\ 1=0$

a)

$23^1=0$

b)

$23^0=1$

c)

$0^{23}=1$

d)

$1^{23}=0$

112.

What is the domain and range of the exponential function y=2^x?

a)

D: $\left(0,\ \infty\right)$

R: $\left(-\infty,\ \infty\right)$

b)

D: $\left(-\infty,\ \infty\right)$

R: $\left(0,\ \infty\right)$

113.

Which graph is representative of the equation?

a)

b)

c)

d)

114.

Which equation is representative of the graph?

a)

y=2(3)^x

b)

y=3(1/2)^x

c)

y=-2(3)^x

115.

Which equation is representative of the graph?

a)

y=4(1/2)^x

b)

y=1/2(4)^x

c)

y=4(2)^x

d)

y=-8(1/2)^x

116.

Is the pictured graph exponential growth, exponential decay, or logarithmic?

a)

Exponential Growth

b)

Exponential Decay

c)

Logarithmic

117.

Is the pictured graph exponential growth, exponential decay, or logarithmic?

a)

Growth

b)

Decay

c)

Logarithmic

118.

Classify the following graph.

a)

Exponential Growth

b)

Exponential Decay

c)

Logarithmic

119.

What is the domain of log(x)?

a)

(-∞, ∞)

b)

(-∞, 0)

c)

(0, ∞)

d)

(0, 8)

120.

What is the range of log(x)?

a)

(-2, 4)

b)

(-∞, ∞)

c)

(-∞, 0)

d)

(0, ∞)

121.

What is the asymptote of the exponential function?

a)

y = 0

b)

y = -3

c)

x = 0

d)

x = -3

122.

What is the asymptote of the logarithmic?

a)

x = 1

b)

y = 1

c)

x = -1

d)

y = -1

123.

Identify the asymptote of the transformed graph $\log_2\left(x+3\right)$ shown in red in the graph

a)

$x=-3$

b)

$x=3$

c)

$y=3$

d)

$y=-3$

124.

What type of function is shown?

a)

exponential

b)

logarithm

c)

quadratic

d)

square root

125.

Classify the following graph.

a)

Exponential Growth

b)

Exponential Decay

c)

Logarithmic

126.

What is the domain?

a)

(-∞, ∞)

b)

(0, ∞)

c)

[1, ∞)

d)

(1, ∞)

127.

What is the asymptote of y = 2^x - 3

a)

y = 0

b)

y = -3

c)

x = 0

d)

x = -3

128.

What is the range of the function graphed?

a)

(-∞, ∞)

b)

(-∞, 2] and [2, ∞)

c)

[2, ∞)

d)

(-∞, 2]

129.

Logarithmic functions are the inverse of...

a)

Linear Functions

b)

Exponential Functions

c)

Quadratic Functions

d)

Polynomial Functions

130.

Is this exponential growth or decay?

a)

Growth

b)

Decay

131.

What is the equation that represents the exponential function in the image below?

a)

y=3(½)^x

b)

y=3(2)^x

c)

y=(2)^x

d)

y=2(3)^x

132.

Using the parent function y=3^x what would the graph of y=3^x+1 look like?

a)

Horizontal shift left one unit

b)

Horizontal shift right one unit

c)

Vertical shift up one unit

d)

Vertical shift down one unit

133.

Select the correct function for the graph.

a)

$f\left(x\right)=\log_2\left(x+3\right)-2$

b)

$f\left(x\right)=\log_2\left(x-3\right)-2$

c)

$f\left(x\right)=2^{\left(x+3\right)}-2$

d)

$f\left(x\right)=2^{\left(x-3\right)}-2$

134.

Select the correct function for the graph.

a)

$f\left(x\right)=\log_2\left(x+3\right)-2$

b)

$f\left(x\right)=\log_2\left(x-3\right)-2$

c)

$f\left(x\right)=2^{\left(x+3\right)}-2$

d)

$f\left(x\right)=2^{\left(x-3\right)}-2$

135.

Select the correct function for the graph.

a)

$f\left(x\right)=\log_2\left(x+3\right)-2$

b)

$f\left(x\right)=\log_2\left(x-3\right)-2$

c)

$f\left(x\right)=2^{\left(x+3\right)}-2$

d)

$f\left(x\right)=2^{\left(x-3\right)}-2$

136.

Select the correct function for the graph.

a)

$f\left(x\right)=\log_2\left(x+3\right)-2$

b)

$f\left(x\right)=\log_2\left(x-3\right)-2$

c)

$f\left(x\right)=2^{\left(x+3\right)}-2$

d)

$f\left(x\right)=2^{\left(x-3\right)}-2$

137.

Select the correct function for the graph.

a)

$f\left(x\right)=\left(\frac{1}{2}\right)^x+3$

b)

$f\left(x\right)=\left(\frac{1}{2}\right)^{\left(x+3\right)}$

c)

$f\left(x\right)=\log_{\frac{1}{2}}\left(x+3\right)$

d)

$f\left(x\right)=\log_{\frac{1}{2}}x+3$

138.

Select the correct function for the graph.

a)

$f\left(x\right)=\left(\frac{1}{2}\right)^x+3$

b)

$f\left(x\right)=\left(\frac{1}{2}\right)^{\left(x+3\right)}$

c)

$f\left(x\right)=\log_{\frac{1}{2}}\left(x+3\right)$

d)

$f\left(x\right)=\log_{\frac{1}{2}}x+3$

139.

Select the correct function for the graph.

a)

$f\left(x\right)=\left(\frac{1}{2}\right)^x+3$

b)

$f\left(x\right)=\left(\frac{1}{2}\right)^{\left(x+3\right)}$

c)

$f\left(x\right)=\log_{\frac{1}{2}}\left(x+3\right)$

d)

$f\left(x\right)=\log_{\frac{1}{2}}x+3$

140.

Select the correct function for the graph.

a)

$f\left(x\right)=\left(\frac{1}{2}\right)^x+3$

b)

$f\left(x\right)=\left(\frac{1}{2}\right)^{\left(x+3\right)}$

c)

$f\left(x\right)=\log_{\frac{1}{2}}\left(x+3\right)$

d)

$f\left(x\right)=\log_{\frac{1}{2}}x+3$

141.

$y=\log_2x-4$

Which statement is true?

a)

This functions shifts down 4

b)

This function shifts up 4

c)

This functions shifts right 4

d)

The asymptote is horizontal

142.

Using the parent function y=2^x what would the graph of y=2^x+ 1 look like?

a)

Horizontal Shift to the right 1 unit

b)

Horizontal shift to the left one unit

c)

Vertical shift one unit up

d)

Vertical shift one unit down

143.

What are the transformations of this graph?

$f\left(x\right)=\log_2\left(x-1\right)+5$

a)

Right 1 Up 5

b)

Right 1 Down 5

c)

Left 1 Up 5

d)

Left 1 Down 5

144.

$f\left(x\right)=\log_2\left(x+3\right)+5$

Describe the asymptote of this function.

a)

vertical

b)

horizontal

c)

there is both a horzontal and vertcal asymptote

145.

Which function has a horizontal asymptote?

a)

exponential

b)

logarithm

c)

both

d)

neither

146.

Which function has a vertical asymptote?

a)

exponential

b)

logarithm

c)

both

d)

neither

147.

Which graph is exponential decay

a)

b)

c)

d)

148.

$y=\left(\frac{1}{2}\right)^{x-5}+3$

Describe the asymptote of this function.

a)

horizontal

b)

vertical

c)

not enough information

149.

Use the function, f(x) = (3/2)^x.
What is the Domain?

a)

(3,2)

b)

(-∞,0)

c)

(-∞,∞)

d)

(0,∞)

150.

Use the function, f(x) = (3/2)^x.
What is the Range?

a)

(3,2)

b)

(-∞,0)

c)

(-∞,∞)

d)

(0,∞)

151.

Determine the horizontal asymptote for the function

f(x) = 3(2)^x-4+ 5

a)

x=4

b)

y=4

c)

x=5

d)

y=5

152.

What is the transformation?
$y=4^{\left(x+5\right)}$

a)

Left 5

b)

Right 5

c)

Up 5

d)

Down 5

153.

find the asymptote: y = log₁₀ (x+3)

a)

x=-3

b)

x=3

c)

y=-3

d)

y=3

154.

Find the asymptote of the following: y = log₁₀x - 6

a)

x=6

b)

x=-6

c)

x= 0

d)

y=0

155.

Domain of $y=\log_6\left(x\right)$ ?

a)

$\left(-\infty,\ \infty\right)$

b)

$\left(0,\ \infty\right)$

c)

$\left(-\infty,\ 0\right)$

d)

$\left[0,\ \infty\right)$

156.

Write the equation of the function f(x)=log₃x after the following transformations:

Translate 6 units left and 4 units up.

a)

g(x)=log₃(x+6)+4

b)

g(x)=log₃(x+4)-6

c)

g(x)=log₃(x-6)+4

d)

g(x)=3log(x+6)+4

157.

What is the domain and range of
f(x) = log ₃ (x + 1)?

a)

D: (− ∞, ∞) R: (−1, ∞)

b)

D: (− ∞, ∞) R: (1, ∞)

c)

D: (−1, ∞) R: (− ∞, ∞)

d)

D: (1, ∞) R: (− ∞, ∞)

158.

Find the asymptote for the following.
$y=\log_3\left(x+1\right)+5$

a)

x = -1

b)

x = 1

c)

y = 5

d)

y = -5

159.

List the range for the following.
$y=\log_3\left(x+1\right)+5$

a)

(-∞,∞)

b)

(-1, ∞)

c)

(5,∞)

d)

(1, ∞)

160.

Find the corresponding graph of
$\log_3\left(x-1\right)+4$

a)

b)

c)

d)

161.

Which graph matches the equation?

a)

b)

c)

d)

162.

Which graph matches this equation?

a)

b)

c)

d)

163.

Which graph matches this equation?

a)

b)

c)

d)

164.

Mrs. W is raising bunnies for Easter. She currently has 5 bunnies and expects the number of bunnies to increase 55% each year. What equation below represents this scenario?

a)

f(x) = 5(155)^t

b)

f(x) = 5(1.55)^t

c)

f(x) = 5(0.155)^t

d)

f(x) = 5(15.5)^t

165.

Mrs. W is raising bunnies for Easter. She currently has 5 bunnies and expects the number of bunnies to increase 55% each year. Approximately how many bunnies would Mrs. W have after 1 year has passed? ( Round to the nearest bunny)

a)

7

b)

17

c)

8

d)

55

166.

Mrs. W is raising bunnies for Easter. She currently has 5 bunnies and expects the number of bunnies to increase 55% each year. Approximately how many bunnies would Mrs. W have after 5 years have passed? ( Round to the nearest bunny)

(a)

167.

Last year, there were 1,500 people who attended the homecoming football game at a local high school. This year, there is expected to be a 16% increase in attendance. What equation represents this scenario?

a)

f(x) = 1,500(11.6)^t

b)

f(x) = 1,500(0.116)^t

c)

f(x) = 1,500(116)^t

d)

f(x) = 1,500(1.16)^t

168.

Last year, there were 1,500 people who attended the homecoming football game at a local high school. This year, there is expected to be a 16% increase in attendance. Based on the equation, approximately how many people will attend homecoming next year? (Round to the nearest person)

a)

1470

b)

1740

c)

240

d)

420

169.

Last year, there were 1,500 people who attended the homecoming football game at a local high school. This year, there is expected to be a 16% increase in attendance. If this trend continues, approximately how many people will attend homecoming in 5 years? (Round to the nearest person)

(a)

170.

The population of Winnemucca, Nevada, can be modeled by P=6191(1.04)^twhere t is the number of years since 1990. What was the population in 1990?

a)

0 people

b)

It doesn't say

c)

I don't know

d)

6191

171.

The population of Winnemucca, Nevada, can be modeled by P=6191(1.04)^t where t is the number of years since 1990. What percent did the population increase each year?

a)

4%

b)

It doesn't say

c)

I don't know

d)

400%

172.

You have inherited land that was purchased for $30,000 in 1960. The value of the land increased by approximately 5% per year. What is the approximate value of the land in the year 2011?

a)

$344,022

b)

$31,500

c)

$15,000

d)

$28,500

173.

The original value of a painting is $1400, and the value increases by 9% each year. Write an exponential growth function to model this situation.

a)

y=1400(1.09)^x

b)

y=1.09(1400)^x

c)

y=1400(.91)^x

d)

y=1.09^x

174.

More and more people are purchasing food from farmers' markets. As a consequence, a market researcher predicts that the number of farmers' markets will increase by 15% each year. If there are 6,200 farmers' markets this year, how many will there be in 10 years? (Round to the nearest whole number if necessary).

a)

25,082

b)

12,937

c)

62,000

d)

43,511

175.

Jenny has $20 in a savings account. The interest rate is 5%, compounded annually. To the nearest cent, how much interest will she earn in 2 years?

a)

$2.05

b)

$45.79

c)

$1.99

d)

$7.51

176.

Does the following equation show growth or decay?
y=10,000*1.26^x

a)

Growth

b)

Decay

177.

Does the following equation show growth or decay?
y=10,000*(0.76)^x

a)

Growth

b)

Decay

178.

Bacteria can multiply at an alarming rate when each bacteria splits into two new cells, thus doubling. If we start with only one bacteria which can double every hour, how many bacteria will we have after half of a day?

a)

1024

b)

2048

c)

8192

d)

4096

179.

The population of Hickory NC, can be modeled by P=6191(1.04)t where t is the number of years since 1995. What was the population in 1995?

a)

6191

b)

1

c)

1995

d)

1.04

180.

Is y = 54(.20)^x growth or decay?

a)

Growth because of the 54

b)

Decay because of the .20

c)

Decay because of the 54

d)

Growth because of the .20

181.

You have inherited land that was purchased for $30,000 in 1990. The value of the land increased by approximately 5% per year. What is the approximate value of the land in the year 2011?

a)

$83,579

b)

$10,217

c)

$14,963,655

d)

$28,500

182.

Is this exponential growth or decay?
y = 7(1.2)^x

a)

Growth, because of 7

b)

Decay, because of 1.2

c)

Growth because of 1.2

d)

Decay because of 7

183.

James' 70 in. giant peach doubles in size every week. Write an expression that would represent how big the peach is after 5 weeks.

a)

y = 70(2)³⁵

b)

y = 70(2)⁵

c)

y = 2(70)⁵

d)

y = 5(70)²

184.

Which of the following functions shows an initial amount of $15 and an increase of 35% each year?

a)

y = 15(35)^x

b)

y = 15(1.35)^x

c)

y = 15(0.35)^x

d)

y = 35(1.15)^x

185.

Write an equation that models the following situation:

Samantha's hair was known to grow very rapidly. It began at a length of 6 in and grew at a rate of 14% a week.

(HINT: Write out the equation on a separate piece of paper and hen simplify inside the parenthesis)

a)

y=6(0.14)^x

b)

y=6(1+14)^x

c)

y=6(1.14)^x

d)

y=6(0.86)^x

186.

Daniel’s Print Shop purchased a new printer for $35,000. Each year it depreciates (loses value) at a rate of 5%.

What is the initial value?

a)

$35,000

b)

0.05

c)

1.05

d)

0.95

187.

Is this exponential growth or decay?
y = 7(1.2)^x

a)

Growth, because of 7

b)

Decay, because of 1.2

c)

Growth because of 1.2

d)

Decay because of 7

188.

The value of a car is $15,000 and depreciates at a rate of 8% per year. What is the exponential equation?

a)

y=8(15,000)^x

b)

y=15,000(1.08)^x

c)

y=15,000(0.92)^x

d)

y=15,000(0.08)^x

189.

James' 70 in. giant peach doubles in size every week. Write an expression that would represent how big the peach is after 5 weeks.

a)

y = 70(2)³⁵

b)

y = 70(2)⁵

c)

y = 2(70)⁵

d)

y = 5(70)²

190.

Write an equation that models the following situation:
Samantha's hair was known to grow very rapidly. It began at a length of 6 in and grew at a rate of 14% a week.

a)

y=6(0.14)^x

b)

y=6(1 + 14)^x

c)

y=6(1 + .14)^x

d)

y=6(0.86)^x

191.

What is the starting amount for the following function:
f(x) = 3(1/3)^x

a)

0

b)

1/3

c)

1

d)

3

192.

Is the pictured graph exponential growth, exponential decay, or linear or none?

a)

Exponential Growth

b)

Exponential Decay

c)

Linear

d)

None of the above

193.

Which of the following functions shows an initial amount of $15 and an increase of 35% each year?

a)

y = 15(35)^x

b)

y = 15(1.35)^x

c)

y = 15(0.35)^x

d)

y = 35(1.15)^x

194.

What is the initial value?

a)

0

b)

3

c)

33

d)

66

195.

Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.

a)

y=5000(0.7)^x

b)

y=30(5000)^x

c)

y=5000(1.3)^x

d)

y=5000x^x

196.

An adult takes 400 mg of ibuprofen. Each hour, the amount of ibuprofen in the person’s system decreases by about 29%.

What would go in the parenthesis for this problem? BEFORE SIMPLIFYING

a)

(1 + 0.29)

b)

(1 - 0.29)

c)

(1 - 0.71)

d)

(1 + 0.71)

197.

You have inherited land that was purchased for $30,000 in 1960. The value of the land increased by approximately 5% per year. What is the approximate value of the land in the year 2011?

a)

$361,223.09

b)

$15,000.00

c)

$31,500.29

d)

$280,500.86

198.

Which of the following functions shows an initial amount of $15 and an increase of 35% each year?

a)

y = 15(35)^x

b)

y = 15(0.35)^x

c)

y = 15(1.35)^x

d)

y = 35(1.15)^x

199.

Is this exponential growth or decay?

a)

Growth because a=1

b)

Growth because there is no a

c)

Decay because b=0.5

d)

Neither because a=0

200.

Is this exponential growth or decay?

a)

Growth, because of 7

b)

Growth because of 1.2

c)

Decay, because of 1.2

d)

Decay because of 7

201.

The value of a car is $15,000 and depreciates at a rate of 8% per year. What is the exponential equation?

a)

y=8(15,000)^x

b)

y=15,000(0.92)^x

c)

y=15,000(1.08)^x

d)

y=15,000(0.08)^x

202.

Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.

a)

y=5000(0.7)^x

b)

y=5000(1.3)^x

c)

y=30(5000)^x

d)

y=5000x^x

203.

The population of Boringtown decreased annually by 1.8% between the year 2015-2018. In 2015, there were approximately 200,000 people living in Boringtown. Which function models the city's population since 2015?

a)

f(x) = 200,000(1 + 0.018)³

b)

f(x) = 200,000(1 - 0.18)³

c)

f(x) = 200,000(1 + 0.18)³

d)

f(x) = 200,000(1 - 0.018)³

204.

A population of amoebas in a petri dish will triple in size every 20 minutes. At the start of an experiment the population is 800. Write a function to model this relationship with y representing the total population, and x as the number of 20 minute periods.

a)

$y=800\left(3\right)^x$

b)

$y=3\left(800\right)^x$

c)

$y=800\left(20\right)^x$

d)

$y=20\left(3\right)^x$

205.

Your shiny new boat cost $7650. The depreciation for your boat is 14% per year. Estimate the value of your vehicle in 3 years. What is the equation that models this problem?

a)

y= 7650(.14)³

b)

y= 7650(.86)³

c)

y= 7650(1+.86/1)^3*1

206.

The value of a car is $15,000 and depreciates at a rate of 8% per year. What is the exponential equation?

a)

y=8(15,000)^x

b)

y=15,000(1.08)^x

c)

y=15,000(0.92)^x

d)

y=15,000(0.08)^x

207.

Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.

a)

y=5000(0.7)^x

b)

y=30(5000)^x

c)

y=5000(1.3)^x

d)

y=5000x^x

208.

The amount of ibuprofen (medicine for headaches) breaks down by 30% each hour. If a person took a 200 milligram ibuprofen, how much will be left after 3 hours?

a)

5.4 mg

b)

68.6 mg

c)

.0054 mg

d)

2,400,000 mg

209.

A sailboat that costs $5,950 decreases in value by 11% per year. How much will the boat be worth after 6 years?

a)

$5,884.00

b)

$5,178.97

c)

$2,992.96

d)

$2,957.04

210.

A 78 gram sample of Uranium loses half of its mass each year. What is the exponential equation?

a)

y=78(0.5)^x

b)

y=78(1.5)^x

c)

y=78(2)^x

211.

The equation y = a(1 - r)^x is used for:

a)

1/2 life

b)

Interest

c)

Exponential Growth

d)

Exponential Decay

212.

The equation y = a(1 + r)^x is used for:

a)

Exponential Growth

b)

Exponential Decay

c)

Half Life

d)

Interest

213.

The Country of Puerto has 3,370,000 people in it and is decreasing at a rate of 4.5%. Estimate the population after 40 years.

a)

534,275

b)

19,601,148

c)

1,350,756

d)

2,521,541

214.

If 10 mg of iodine 131 is given to a patient, how much is left after 24 days? The half-life of iodine-131 is 8 days.

a)

1.25mg

b)

1.25g

c)

10g

d)

10mg

215.

Given the following equation
$y=320\left(\frac{1}{2}\right)^{\frac{5}{8}}$
Which is true?

a)

320 is the amount of time it takes for the value to be at half the original amount.

b)

1/2 is the amount of time it takes for the value to be at half the original amount.

c)

5 is the amount of time it takes for the value to be at half the original amount.

d)

8 is the amount of time it takes for the value to be at half the original amount.

216.

Prescription A has an initial value of 1200 mg/L and a half-life 6 hours. Which equation will help us determine the remaining level after 1 day?

a)

$y=1200\left(\frac{1}{2}\right)^{\frac{1}{6}}$

b)

$y=1200\left(\frac{1}{2}\right)^{\frac{24}{6}}$

c)

$y=1200\left(\frac{1}{2}\right)^{\frac{6}{1}}$

d)

$y=1200\left(\frac{1}{2}\right)^{\frac{6}{24}}$

217.

Bruno was given $2000 when he turned 3 years old. His parents invested it at a 2% interest rate compounded annually. No deposits or withdrawls were made. Which expression can be used to determine how much money Bruno had in the account when he turned 16?

a)

2000(1+0.02)¹³

b)

2000(1-0.02)¹³

c)

2000(1+0.02)¹⁶

d)

2000(1-0.02)¹⁶

218.

The compound interest formula is:

F = P(1 + r)^t

What does the F represent?

a)

The amount of interest earned.

b)

The amount of time that has passed.

c)

The total amount of money after a certain amount of time.

d)

The amount required to invest.

219.

Caiden earned $475 from mowing lawns last summer. He deposited this money in an account that pays an interest rate of 3.8% compounded annually. What will be his balance after 15 year?

a)

$827.52

b)

$831.10

c)

$839.45

d)

$846.80

220.

How many times does compounded semi-annually a year mean?

a)

4

b)

12

c)

52

d)

2

221.

The expression (1.016)^t/3 represents the interest that a bank pays on a savings account. What is the yearly interest rate?

a)

0.5%

b)

1.05%

c)

1.6%

d)

.04%

222.

You want to save $5,000 for future family vacation. If you assume you can get an interest rate of 4.3% compounded monthly, then how much will you need to invest NOW to reach your vacation goal in 3 years?

a)

$307,042,791

b)

$5,000

c)

$3,250

d)

$4,395.89

223.

Principal: $5000

Interest Rate: 3.75%

Time: 25 years

Compounded Monthly

State the ending account balance.

a)

$12712.31

b)

$12,749.30

c)

$12,657.59

d)

$12550.84

224.

In the compound interest formula A=P(1+r)^t what does the P stand for?

a)

The time

b)

The total final amount

c)

The principal amount (original amount)

d)

The interest rate

225.

In the compound interest formula A=P(1+r)^t what does the A stand for?

a)

The amount of interest

b)

The total final amount

c)

The interest rate

d)

The time

226.

Emily would like to buy some new furniture for her home. She decides to buy the furniture on credit with 9.5% interest compounded quarterly. If she spent $7,400, how much total will she have paid after 8 years?

a)

$15,415.94

b)

$15,683.28

c)

$15,927.56

d)

$16,109.05

227.

Johnny takes an unknown amount of money and deposits it in a bank at an interest rate of 2%. He leaves the money in the account for 6 years, compounded quarterly. If the Johnny withdraws after 6 years is $455,125, what was the original amount of money he deposited?

a)

$403 780

b)

$404 138

c)

$406 362

d)

$436 870

228.

Treasure won $3,000 from a radio contest. If she puts this money in a bank account that earns 2.9% interest compounded quarterly, how much total will she have in 10 years?

a)

$4915.59

b)

$3933.28

c)

$2979.81

d)

$4005.09

229.

Zach's parents put $1,500 in his bank account for college tuition. At an interest rate of 8.25% compounded semi-annually, what will be the balance after 18 years?

a)

$6,273.50

b)

$6,314.08

c)

$6,385.72

d)

$6,427.94

230.

Heather invested $8,000 in a 4-year Certificate of Deposit (CD) that pays 4.1% interest compounded annually. What is the value of the CD at the end of the 4 years?

a)

$9,394.92

b)

$9,312.00

c)

$1394.00

d)

$1312.00

231.

Riley invested $1,000 in savings bonds. If the bonds earn 6.75% interest compounded semi-annually, how much total will Riley earn in 15 years?

a)

$1,584.62

b)

$2,651.39

c)

$2,706.86

d)

$1,825.10

232.

Olivia would like to buy some new furniture for her home. She decides to buy the furniture on credit with 9.5% interest compounded quarterly. If she spent $7,400, how much total will she have paid after 8 years.

a)

$15,415.94

b)

$15,683.28

c)

$15,927.56

d)

$16,109.05

233.

Write the equation that fits the description:

Investment $1000

Compound Interest Rate 6%

a)

$A=1000\left(1.06\right)^n$

b)

A = 100 + 6n

c)

A = 1000 + 60n

d)

$A=1000\left(0.06\right)^n$

234.

Growth or Decay?

$y=1200\left(1+0.03\right)^t$

a)

Growth

b)

Decay

235.

What is the rate of growth?

$y=1200\left(1+0.03\right)^t$

a)

Growth

b)

1200

c)

0.03

d)

Decay

236.

What is the decay rate?

$y=55\left(1-0.02\right)^t$

a)

Growth

b)

Decay

c)

55

d)

0.02

237.

Q = 3.1(0.78)^t

What is the DECAY rate?

Write as a percent!

CAREFUL!!!

(a)

238.

Q = 3.1(0.78)^t

What is the initial quantity?

(a)

239.

North Dakota has recently had the fastest growing population out of all 50 states. On Jan 1, 2013, the population of North Dakota was 700,000 people. North Dakota’s population has been growing by 5% per year. Express North Dakota’s population, N, in terms of years since 2013, t.

Check the BEST answer:

a)

N=700,000(1.05)t

b)

N=700,000(1.5)t

c)

N=700,000(1-0.05)^t

d)

N=700,000(0.95)^t

240.

An air freshener starts with 30 grams of fluid, and the amount of fluid decreases by 12% per day. Express the amount of grams of freshener, Q, that remains, t, days after it has begun being used.

Check the BEST answer: (HINT: that means simplify what is in the parenthesis)

a)

Q=30(1+0.12)^t

b)

Q=30(1-0.12)^t

c)

Q=30(0.88)^t

d)

Q=12(1.30)^t

241.

A population of bees starts out with 10 bees and doubles every day.

a)

$y=10\left(2\right)^x$

b)

$y=10\left(2\right)^{\frac{x}{2}}$

c)

$y=2\left(10\right)^x$

d)

$y=10\left(\frac{1}{2}\right)^x$

242.

A NCAA tournament starts out with 64 teams. Every round half the teams are eliminated.

a)

$y=64\left(2\right)^x$

b)

$y=64\left(\frac{1}{2}\right)^2$

c)

$y=64\left(\frac{1}{2}\right)^x$

d)

$y=64\left(2\right)^{\frac{x}{2}}$

243.

Bacteria on old cheese starts out with 15 bacteria and triples every 2 hours.

a)

$y=15\left(3\right)^x$

b)

$y=15\left(3\right)^{\frac{2}{x}}$

c)

$y=3\left(15\right)^{\frac{x}{2}}$

d)

$y=15\left(3\right)^{\frac{x}{2}}$

244.

The population of carp is cut in half every day. The population starts out with 1500 carp.

a)

$y=1500\left(\frac{1}{2}\right)^x$

b)

$y=1500\left(2\right)^x$

c)

$y=1500\left(\frac{1}{2}\right)^{\frac{x}{2}}$

d)

$y=\frac{1}{2}\left(1500\right)^x$

245.

Which equation is an exponential equation?

a)

$y=3x+15$

b)

$y=0.5x+10$

c)

$y=3\left(2\right)^x$

d)

$y=300-10x$

246.

A population of ants quadruples every day. Initially, there are 10 ants.

a)

$y=4\left(10\right)^x$

b)

$y=10\left(x\right)^4$

c)

$y=10\left(4\right)^x$

d)

$y=10\left(4x\right)$

247.

A tennis tournament starts out with 128 teams and the teams are eliminated by half each round.

a)

$y=128\left(.5\right)^{\frac{x}{1}}$

b)

$y=128\left(2\right)^{\frac{x}{1}}$

c)

$y=.5\left(128\right)^{\frac{x}{1}}$

d)

$y=128\left(.5\right)^{\frac{x}{2}}$

248.

The bacteria on an old pizza starts out with 5 bacteria and doubles every 4 days.

a)

$y=4\left(2\right)^{\frac{x}{5}}$

b)

$y=5\left(2\right)^{\frac{x}{4}}$

c)

$y=2\left(5\right)^{\frac{x}{4}}$

d)

$y=5\left(4\right)$

249.

A wishing well starts out with 40 coins and triples every day.

a)

$y=5\left(40\right)^x$

b)

$y=40\left(3\right)^x$

c)

$y=3\left(5\right)^{40}$

d)

$y=40\left(3\right)^{\frac{x}{3}}$

250.

A type of bacteria doubles every 4 hours. A Petri dish starts out with 16 of these bacteria.

a)

$y=2\left(16\right)^{\frac{x}{4}}$

b)

$y=16\left(2\right)^{\frac{x}{4}}$

c)

$y=16\left(4\right)^{\frac{x}{2}}$

d)

$y=16\left(2\right)^x$

251.

Evaluate the function for the given value:

f (x) = 5^x for f(4)

a)

20

b)

625

c)

125

d)

25

252.

Evaluate the function for the given value:

h(t) = 3 • 4^t for h(-3)

a)

$\frac{3}{64}$

b)

192

c)

-36

d)

$-\frac{3}{64}$

253.

Evaluate the function for the given value:

$y=8\cdot0.7^x$ for x = 3

a)

2.744

b)

175,616

c)

16.8

d)

432,8

254.

Evaluate the function for the given value:

$f\left(x\right)=3^x$ for f(3)

a)

27

b)

9

c)

6

d)

12

255.

Evaluate the function for the given value:

y=\left(\frac{1}{4}\right)^x

for x = 4

a)

$\frac{1}{256}$

b)

256

c)

$\frac{1}{16}$

d)

16

256.

An investment of $8000 in a certain Certificate of Deposit (CD) doubles in value every seven years. The function that models the growth of this investment is f (x) = 8000(2)^x, where x is the number of 7 year periods. If the investor does not withdraw any money from this CD, how much money will be available for withdrawal after 28 years?

a)

$128,000

b)

$1,024,000

c)

$2,147,483,648,000

d)

$112,000

257.

A population of amoebas in a petri dish will triple in size every 20 minutes. At the start of an experiment the population is 800. Write a function to model this relationship with y representing the total population, and x as the number of 20 minute periods.

a)

$y=800\left(3\right)^x$

b)

$y=3\left(800\right)^x$

c)

$y=800\left(20\right)^x$

d)

$y=20\left(3\right)^x$

258.

A population of amoebas in a petri dish will triple in size every 20 minutes. At the start of an experiment the population is 800. Write a function to model this relationship with y representing the total population, and x as the number of 20 minute periods. How many amoebas are in the petri dish after 3 hours?

a)

15,746,400

b)

216,000

c)

27,894,275,208,000

d)

67.893

259.

A new car costs $15,000 to build in 2010. The company’s financial analysts expect costs to rise by 6% per year for the 10 years they are planning to build the car. The cost to build the car can be modeled by the function f (t) = 15,000 (1.06)^t , where t is the number of years after 2010. How much will it cost the company to build the car in 2017?

a)

$22,554.45

b)

$23,907.72

c)

$19,678.32

d)

$45,678.91

260.

Linear, exponential, or neither?

y = 4 + 2x

a)

Linear

b)

Exponential

c)

Neither

261.

Linear, exponential, or neither?

y = 4(3)^x

a)

Linear

b)

Exponential

c)

Neither

262.

Linear, exponential, or neither?

Amount increases $10 per year

a)

Linear

b)

Exponential

c)

Neither

263.

Linear, exponential, or neither?

Amount triples each year

a)

Linear

b)

Exponential

c)

Neither

264.

Linear, exponential, or neither?

a)

Linear

b)

Exponential

c)

Neither

265.

Linear, exponential, or neither?

a)

Linear

b)

Exponential

c)

Neither

266.

Linear, Exponential, or Neither?

There are 800 students at Western Middle. The population increases by 3% each year.

a)

Linear

b)

Exponential

c)

Neither

267.

Write a function to represent:

A petri dish contains 35 bacteria. The bacteria triple every hour.

a)

$y=35\left(3\right)^x$

b)

$y=3\left(35\right)^x$

c)

$y=35\left(\frac{1}{3}\right)^x$

d)

$y=35\left(x\right)^3$

268.

Write a function to represent the following function:

A hospital prepares a 100 mg supply of technetium‐99m which has a half‐life of 6 hours.

a)

$f\left(x\right)=100\left(\frac{1}{2}\right)^x$

b)

$f\left(x\right)=99\left(\frac{1}{2}\right)^x$

c)

$f\left(x\right)=100\left(6\right)^x$

d)

$f\left(x\right)=100\left(99\right)^x$

269.

A hospital prepares a 100 mg supply of technetium‐99m which has a half‐life of 6 hours. How many mg are left after one day?

a)

6.25 mg

b)

12 mg

c)

0.00125 mg

d)

3.125 mg

270.

A petri dish contains 35 bacteria. The bacteria triple every hour. How many bacteria are present after 4 hours?

a)

2835 bacteria

b)

945 bacteria

c)

1563 bacteria

d)

3685 bacteria

Exponential & Logarithmic Quest Practice Problems

Total questions: 270

Worksheet time: 16hrs 44mins