Deck 9: Exponential and Logarithmic Functions
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Deck 9: Exponential and Logarithmic Functions
1
Identify the horizontal asymptote of .
A)
B)x -axis
C) y=-7
D) y=7
E)
A)
B)x -axis
C) y=-7
D) y=7
E)
y=7
2
Match with its graph.
A)
B)
C)
D)
E)
A)

B)

C)

D)

E)


3
Identify the horizontal asymptote of .
A)x -axis
B) y=2
C) y=-2
D) y=16
E) y=-16
A)x -axis
B) y=2
C) y=-2
D) y=16
E) y=-16
x -axis
4
Sketch the graph of the function .
A)
B)
C)
D)
E)
A)

B)

C)

D)

E)

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5
Evaluate the function as indicated. Round to three decimal places if necessary.
A)10,303.010
B)10,936.853
C)91,999.387
D)4702.847
E)90,900.000
A)10,303.010
B)10,936.853
C)91,999.387
D)4702.847
E)90,900.000
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6
Evaluate the function as indicated. Round your answer to three decimal places.
A)-0.588
B)0.588
C)2.700
D)1.700
E)-1.700
A)-0.588
B)0.588
C)2.700
D)1.700
E)-1.700
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7
Evaluate the function as indicated. Round your answer to three decimal places.
A)0.500
B)0.667
C)2.500
D)-0.667
E)-1.500
A)0.500
B)0.667
C)2.500
D)-0.667
E)-1.500
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8
Match with its graph.
A)
B)
C)
D)
E)
A)

B)

C)

D)

E)

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9
A)
B)
C)
D)
E)cannot be simplified
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10
Evaluate the expression . Round your answer to three decimal places.
A)8.485
B)3.000
C)12.603
D)2.449
E)22.274
A)8.485
B)3.000
C)12.603
D)2.449
E)22.274
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11
Simplify the expression.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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12
Simplify the expression.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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13
Simplify the expression.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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14
Evaluate the function as indicated. Round to three decimal places if necessary.
A)13,107.960
B)1310.796
C)10,700.000
D)42,800.000
E)44,076.205
A)13,107.960
B)1310.796
C)10,700.000
D)42,800.000
E)44,076.205
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15
Evaluate the function as indicated. Round to three decimal places if necessary.
A)212,352.559
B)227981.657
C)16,063.706
D)41,451.210
E)179,850.000
A)212,352.559
B)227981.657
C)16,063.706
D)41,451.210
E)179,850.000
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16
Evaluate the function as indicated. Round your answer to three decimal places.
A)-6.767
B)6.767
C)-904.837
D)369.453
E)210.588
A)-6.767
B)6.767
C)-904.837
D)369.453
E)210.588
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17
Evaluate the function as indicated. Round your answer to three decimal places.
A)-1087.313
B)1.832
C)5459.815
D)1.593
E)-485.225
A)-1087.313
B)1.832
C)5459.815
D)1.593
E)-485.225
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18
Evaluate the function as indicated. Round your answer to three decimal places.
A)-9.473
B)10.705
C)-169.829
D)9.473
E)517.234
A)-9.473
B)10.705
C)-169.829
D)9.473
E)517.234
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19
Evaluate the function as indicated. Round your answer to three decimal places.
A)0.399
B)-2.944
C)-0.032
D)2.507
E)not a real number
A)0.399
B)-2.944
C)-0.032
D)2.507
E)not a real number
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20
Identify the horizontal asymptote of .
A)
B)
C)
D) y=15
E)x -axis
A)
B)
C)
D) y=15
E)x -axis
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21
After t years, the remaining mass y (in grams)of 24 grams of a radioactive elements whose half-life is 30 years is given by . How much of the initial mass remains after 50 years? Round your answers to two decimal places.
A)7.56 grams
B)14.40 grams
C)3.17 grams
D)16.44 grams
E)nothing remains
A)7.56 grams
B)14.40 grams
C)3.17 grams
D)16.44 grams
E)nothing remains
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22
The population P (in millions)of the United States from 1970 to 2000 can be approximated by the exponential function , where t is the time in years with corresponding to 1970. Use the model to estimate the population in the year 2,005. Round your answer to one decimal place. Source: U.S. Census Bureau
A)205.2 million
B)7,181.0 million
C)223.9million
D)294.6 million
E)1.5 million
A)205.2 million
B)7,181.0 million
C)223.9million
D)294.6 million
E)1.5 million
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23
Find where and .
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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24
Determine the principal P (to the nearest cent)that will yield a balance of
dollars when invested at rate
for 40 years, compounded once per year. Round the answer to two decimal places.
A)$56,306.31
B)$568,181.82
C)$68,460.62
D)$55,625.00
E)$38,461.03


A)$56,306.31
B)$568,181.82
C)$68,460.62
D)$55,625.00
E)$38,461.03
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25
The value of a piece of property doubles every 16 years. You buy the property for $50,000. Its value t years after the date of purchase should be . Use the model to approximate (to the nearest thousand dollars)the value of the property after 4 years.
A)$50,000
B)$6,400,000
C)$75,000
D)$59,000
E)$100,000
A)$50,000
B)$6,400,000
C)$75,000
D)$59,000
E)$100,000
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26
Determine the principal P (to the nearest cent)that will yield a balance of dollars when invested at rate for 40 years, compounded continuously. Round the answer to two decimal places.
A)$611,887.72
B)$495,364.63
C)$16,686.63
D)$13,015.58
E)$13,608.96
A)$611,887.72
B)$495,364.63
C)$16,686.63
D)$13,015.58
E)$13,608.96
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27
Determine the principal P (to the nearest cent)that will yield a balance of dollars when invested at rate for 40 years, compounded 12 times per year. Round the answer to two decimal places.
A)$973.96
B)$273,927.55
C)$16,025.64
D)$37,398.27
E)$402,834.63
A)$973.96
B)$273,927.55
C)$16,025.64
D)$37,398.27
E)$402,834.63
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28
Determine the balance A ( to the nearest cent)for
dollars invested at a rate
for
, compounded 365 times per year. Round the answer to two decimal places.
A)$9,855.00
B)$8,042.90
C)$7,378.81
D)$6,027.12
E)$7,377.99



A)$9,855.00
B)$8,042.90
C)$7,378.81
D)$6,027.12
E)$7,377.99
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29
Find where and .
A)24
B)-29
C)4
D)28
E)-11
A)24
B)-29
C)4
D)28
E)-11
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30
Identify the transformation of .
A)a shift of 6 units downward
B)a shift of 6 units to the left
C)a reflection about the line x=6
D)a shift of 6 units to the right
E)a shift of 6 units upward
A)a shift of 6 units downward
B)a shift of 6 units to the left
C)a reflection about the line x=6
D)a shift of 6 units to the right
E)a shift of 6 units upward
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31
Find where and .
A)12
B)15
C)-28
D)-8
E)-34
A)12
B)15
C)-28
D)-8
E)-34
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32
Find where and .
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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33
Determine the principal P (to the nearest cent)that will yield a balance of dollars when invested at rate for 40 years, compounded 365 times per year. Round the answer to two decimal places.
A)$38,920.73
B)$1,541,095.89
C)$1,712.33
D)$2,472,756.03
E)$45,814.19
A)$38,920.73
B)$1,541,095.89
C)$1,712.33
D)$2,472,756.03
E)$45,814.19
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34
Determine the balance A ( to the nearest cent)for
dollars invested at a rate
for
, compounded continuously. Round the answer to two decimal places.
A)$8,154.85
B)$10,950.00
C)$8,153.73
D)$8,887.56
E)$6,030.15



A)$8,154.85
B)$10,950.00
C)$8,153.73
D)$8,887.56
E)$6,030.15
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35
Determine the balance A ( to the nearest cent)for
dollars invested at a rate
for
, compounded one time per year. Round the answer to two decimal places.
A)$33,000.00
B)$4,781.23
C)$3,000.00
D)$6,000.00
E)$7,781.23



A)$33,000.00
B)$4,781.23
C)$3,000.00
D)$6,000.00
E)$7,781.23
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36
Determine the balance A ( to the nearest cent)for
dollars invested at a rate
for
, compounded 12 times per year. Round the answer to two decimal places.
A)$529.94
B)$4,700.00
C)$1,126.10
D)$1,004.83
E)$6,359.33



A)$529.94
B)$4,700.00
C)$1,126.10
D)$1,004.83
E)$6,359.33
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37
Find where and .
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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38
Determine the balance A ( to the nearest cent)for
dollars invested at a rate
for
, compounded 4 times per year. Round the answer to two decimal places.
A)$3,161.40
B)$12,000.00
C)$12,645.59
D)$94,298.50
E)$6,392.88



A)$3,161.40
B)$12,000.00
C)$12,645.59
D)$94,298.50
E)$6,392.88
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39
Identify the transformation of .
A)a reflection about the y -axis
B)a reflection about the x -axis
C)a reflection about the line y=-x
D)a reflection about the line y=x
E)a reflection about the line x=15
A)a reflection about the y -axis
B)a reflection about the x -axis
C)a reflection about the line y=-x
D)a reflection about the line y=x
E)a reflection about the line x=15
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40
Determine the principal P (to the nearest cent)that will yield a balance of
dollars when invested at rate
for 40 years, compounded 4 times per year. Round the answer to two decimal places.
A)$173,611.11
B)$14,218.75
C)$1,026,614.38
D)$147,569.44
E)$71,090.14


A)$173,611.11
B)$14,218.75
C)$1,026,614.38
D)$147,569.44
E)$71,090.14
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41
Use the function of and to find the value of .
A)4
B)3
C)-3
D)2
E)-2
A)4
B)3
C)-3
D)2
E)-2
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42
Find the inverse function of .
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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43
Find the inverse function of .
A)
B)
C)
D)
E)The function does not have an inverse.
A)
B)
C)
D)
E)The function does not have an inverse.
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44
Use the horizontal Line Test to determine if the function is one-to-one and so has an inverse function.

A)f is one-to-one
B)f is not one-to-one
C)cannot be determined

A)f is one-to-one
B)f is not one-to-one
C)cannot be determined
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45
Which statement(s)verify that and are inverse?
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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46
Find the domain of where and .
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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47
Find the domain of where and .
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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48
Use the horizontal Line Test to determine if the function is one-to-one and so has an inverse function.

A)f is one-to-one
B)f is not one-to-one
C)cannot be determined

A)f is one-to-one
B)f is not one-to-one
C)cannot be determined
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49
Which statement(s)verify that and are inverse?
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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50
Find where and .
A)73
B)115
C)223
D)61
E)-9
A)73
B)115
C)223
D)61
E)-9
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51
Find the domain of where and .
A)
B)
C)
D)
E) .
A)
B)
C)
D)
E) .
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52
Find where and .
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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53
Find the inverse function of .
A)
B)
C)
D)
E)The function does not have an inverse.
A)
B)
C)
D)
E)The function does not have an inverse.
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54
Find the domain of where and .
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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55
Find where and .
A)-16
B)2
C)1
D)-15
E)-5
A)-16
B)2
C)1
D)-15
E)-5
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56
Find where and .
A)-64
B)-26
C)-5
D)-192
E)1
A)-64
B)-26
C)-5
D)-192
E)1
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57
Which statement(s)verify that and are inverse?
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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58
Find where and .
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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59
Find where and .
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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60
Find where and .
A)32
B)38
C)146
D)132
E)26
A)32
B)38
C)146
D)132
E)26
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61
Match with its graph.
A)
B)
C)
D)
E)
A)

B)

C)

D)

E)

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62
Match with its graph.
A)
B)
C)
D)
E)
A)

B)

C)

D)

E)

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63
Write the exponential equation in logarithmic form.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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64
Identify the vertical asymptote of .
A) t=5
B)
C)
D) t=-5
E)y -axis
A) t=5
B)
C)
D) t=-5
E)y -axis
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65
Evaluate the logarithm.
A)
B) 3
C) 2
D)
E) is undefined.
A)
B) 3
C) 2
D)
E) is undefined.
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66
Use a calculator to evaluate the common logarithm . Round your answer to four decimal places.
A)1.6812
B)1.6721
C)3.8501
D)1.9777
E)3.8712
A)1.6812
B)1.6721
C)3.8501
D)1.9777
E)3.8712
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67
Match the graph with the graph of its inverse function. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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68
Find the inverse function of .
A)
B)
C)
D)
E)The function does not have an inverse.
A)
B)
C)
D)
E)The function does not have an inverse.
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69
Evaluate the logarithm.
A)
B)1
C) -1
D)0
E)Undefined
A)
B)1
C) -1
D)0
E)Undefined
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70
Identify the vertical asymptote of .
A) t=-6
B) t=6
C) t=7
D) t=-7
E)y -axis
A) t=-6
B) t=6
C) t=7
D) t=-7
E)y -axis
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71
Match the graph with the graph of its inverse function. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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72
Match the graph with the graph of its inverse function. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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73
Evaluate the logarithm.
A)
B)3
C)
D)6
E) is undefined.
A)
B)3
C)
D)6
E) is undefined.
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74
Match with its graph.
A)
B)
C)
D)
E)
A)

B)

C)

D)

E)

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75
Match with its graph.
A)
B)
C)
D)
E)
A)

B)

C)

D)

E)

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76
Evaluate the logarithm.
A) -3
B)9
C)
D)3
E) is undefined.
A) -3
B)9
C)
D)3
E) is undefined.
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Unlock for access to all 165 flashcards in this deck.
Unlock Deck
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77
Evaluate the logarithm.
A)0
B)
C) -1
D)
E) is undefined.
A)0
B)
C) -1
D)
E) is undefined.
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Unlock for access to all 165 flashcards in this deck.
Unlock Deck
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78
Write the logarithmic equation in exponential form.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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Unlock Deck
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79
Evaluate the logarithm.
A)
B) -3
C)0
D)
E) is undefined.
A)
B) -3
C)0
D)
E) is undefined.
Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck
80
Match the graph with the graph of its inverse function. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

Unlock Deck
Unlock for access to all 165 flashcards in this deck.
Unlock Deck
k this deck