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Deck 4: Exponential and Logarithmic Functions
Full screen (f)
Question
Determine whether the function has an inverse function, If it does, find its inverse function. 
A) No,
does not have an inverse function.
B) Yes,
has an inverse function, 
C) Yes,
has an inverse function, 
D) Yes,
has an inverse function, 
E) Yes,
has an inverse function, 
A) No,
does not have an inverse function.B) Yes,
has an inverse function, C) Yes,
has an inverse function, D) Yes,
has an inverse function, E) Yes,
has an inverse function, 
Question
The demand function for a limited edition comic book is given by 
Find the price 
for a demand of 
units.
A) $5789.56
B) $258.96
C) $312.99
D) $6312.99
E) $210.44
Find the price for a demand of units.A) $5789.56
B) $258.96
C) $312.99
D) $6312.99
E) $210.44
Question
Evaluate the expression below.Round your results to three decimal places. 
A) 0.135
B) 0.018
C) 54.598
D) 0.050
E) 0.007
A) 0.135
B) 0.018
C) 54.598
D) 0.050
E) 0.007
Question
Determine whether the function has an inverse function, If it does, find its inverse function. 
A) No,
does not have an inverse function.
B) Yes,
has an inverse function, 
C) Yes,
has an inverse function, 
D) Yes,
has an inverse function, 
E) Yes,
has an inverse function, 
A) No,
does not have an inverse function.B) Yes,
has an inverse function, C) Yes,
has an inverse function, D) Yes,
has an inverse function, E) Yes,
has an inverse function, Question
Use the functions given by 
and 
to find the composition of functions 
A)
B)
C)
D)
E)
and to find the composition of functions A)
B)
C)
D)
E)
Question
Use the graph of 
to determine whether the function has an inverse function. 
A) Yes,
has an inverse function.
B) No,
does not have an inverse function.
to determine whether the function has an inverse function. A) Yes,
has an inverse function.B) No,
does not have an inverse function. Question
A company's profit 
for producing 
units is given by 
Find the inverse function 
and explain what it represents.Describe the domains of 
and 
A)
, 
represents the number of units that must be sold to obtain the profit of 
Domain of 
, Domain of 
B)
, 
represents the number of units that must be sold to obtain the profit of 
Domain of 
, Domain of 
C)
, 
represents the number of units that must be sold to obtain the profit of 
Domain of 
, Domain of 
D)
, 
represents the number of units that must be sold to obtain the profit of 
Domain of 
, Domain of 
E)
, 
represents the number of units that must be sold to obtain the profit of 
Domain of 
, Domain of 
for producing units is given by Find the inverse function and explain what it represents.Describe the domains of and A)
, represents the number of units that must be sold to obtain the profit of Domain of , Domain of B)
, represents the number of units that must be sold to obtain the profit of Domain of , Domain of C)
, represents the number of units that must be sold to obtain the profit of Domain of , Domain of D)
, represents the number of units that must be sold to obtain the profit of Domain of , Domain of E)
, represents the number of units that must be sold to obtain the profit of Domain of , Domain of Question
Use the functions given by 
and 
to find the value 
A) 1
B) 0
C) 3
D) 4
E) 2
and to find the value A) 1
B) 0
C) 3
D) 4
E) 2
Question
Sketch the graph of the function 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use the graph of 
to determine whether the function has an inverse function. 
A) No,
does not have an inverse function.
B) Yes,
has an inverse function.
to determine whether the function has an inverse function. A) No,
does not have an inverse function.B) Yes,
has an inverse function. Question
Use the functions given by 
and 
to find the value 
A) 16
B) -16
C) 32
D) The value does not exist.
E) -32
and to find the value A) 16
B) -16
C) 32
D) The value does not exist.
E) -32
Question
Find the inverse function informally 
Verify that 
and 
A)
, 
, 
B)
, 
, 
C)
, 
, 
D)
, 
, 
E)
, 
, 
Verify that and A)
, , B)
, , C)
, , D)
, , E)
, , Question
Use the functions given by 
and 
to find the composition of functions 
A)
B)
C)
D)
E)
and to find the composition of functions A)
B)
C)
D)
E)
Question
Use the functions given by 
and 
to find the value 
A) 32
B) 35
C) 33
D) 37
E) 30
and to find the value A) 32
B) 35
C) 33
D) 37
E) 30
Question
Show that 
and 
are functions by using the definition of inverse functions. 
A)
B)
C)
D)
E)
and are functions by using the definition of inverse functions. A)
B)
C)
D)
E)
Question
Show that 
and 
are functions by using the definition of inverse functions. 
A)
B)
C)
D)
E)
and are functions by using the definition of inverse functions. A)
B)
C)
D)
E)
Question
Find the inverse function of the function f given by the set of ordered pairs. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Determine which of the following functions is graphed below. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the inverse function informally 
Verify that 
and 
A)
, 
, 
B)
, 
, 
C)
, 
, 
D)
, 
, 
E)
, 
, 
Verify that and A)
, , B)
, , C)
, , D)
, , E)
, , Question
Find the inverse function of the function f given by the set of ordered pairs. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Sketch the graph of the function 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Write the logarithmic equation 
in its exponential form.
A)
B)
C)
D)
E)
in its exponential form.A)
B)
C)
D)
E)
Question
Match the function 
with its graph.
A)
B)
C)
D)
E)
with its graph.A)
B)
C)
D)
E)
Question
Find the vertical asymptote of the logarithmic function below. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Evaluate the logarithm 
without using a calculator.
A)
B)
C)
D)
E)
without using a calculator.A)
B)
C)
D)
E)
Question
Use a calculator to evaluate 
Round your result to three decimal places.
A)
B)
C)
D)
E)
Round your result to three decimal places.A)
B)
C)
D)
E)
Question
Sketch the graph of the function 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Match the function below with its graph. 
Graph I : 
Graph IV: 
Graph II: 
Graph V: 
Graph III: 
A) Graph II
B) Graph V
C) Graph I
D) Graph IV
E) Graph III
Graph I : Graph IV: Graph II: Graph V: Graph III: A) Graph II
B) Graph V
C) Graph I
D) Graph IV
E) Graph III
Question
Sketch the graph of the function 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use a calculator to evaluate 
Round your result to three decimal places.
A)
B)
C)
D)
E)
Round your result to three decimal places.A)
B)
C)
D)
E)
Question
Rewrite the logarithmic equation 
in exponential form.
A)
B)
C)
D)
E)
in exponential form.A)
B)
C)
D)
E)
Question
Use a calculator to evaluate the function 
for the given value of 
, 
Round your result to three decimal places.
A)
B)
C)
D)
E)
for the given value of , Round your result to three decimal places.A)
B)
C)
D)
E)
Question
Use a calculator to evaluate the function 
for the given value of 
, 
Round your result to three decimal places.
A)
B)
C)
D)
E)
for the given value of , Round your result to three decimal places.A)
B)
C)
D)
E)
Question
Write the logarithmic equation 
in exponential form.
A)
B)
C)
D)
E)
in exponential form.A)
B)
C)
D)
E)
Question
Sketch the graph of the function 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Rewrite the exponential equation 
in logarithmic form.
A)
B)
C)
D)
E)
in logarithmic form.A)
B)
C)
D)
E)
Question
Find the domain of the function 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Write the exponential equation 
in its logarithmic form.
A)
B)
C)
D)
E)
in its logarithmic form.A)
B)
C)
D)
E)
Question
Write the exponential equation 
in logarithmic form.
A)
B)
C)
D)
E)
in logarithmic form.A)
B)
C)
D)
E)
Question
Match the function 
with its graph.
A)
B)
C)
D)
E)
with its graph.A)
B)
C)
D)
E)
Question
Write 
as a single logarithm with a coefficient of 1. Assume all variable expressions represent positive real numbers.
A)
B)
C)
D)
E)
as a single logarithm with a coefficient of 1. Assume all variable expressions represent positive real numbers.A)
B)
C)
D)
E)
Question
Expand the logarithmic expression 
Assume all variable expressions represent positive real numbers.
A)
B)
C)
D)
E)
Assume all variable expressions represent positive real numbers.A)
B)
C)
D)
E)
Question
Solve for x. 
A)
B)
C)
D)
E) 2
A)
B)
C)
D)
E) 2
Question
The present value of money is the principal 
you need to invest today so that it will grow to an amount 
at the end of specified time.The present value formula 
is obtained by solving the compound interest formula 
for 
Recall that 
is the number of years, 
is the interest rate per year, and 
is the number of compoundings per year.find the present value of amount 
invested at rate 
for 
years, compounded 
times per year. 
A)
B)
C)
D)
E)
you need to invest today so that it will grow to an amount at the end of specified time.The present value formula is obtained by solving the compound interest formula for Recall that is the number of years, is the interest rate per year, and is the number of compoundings per year.find the present value of amount invested at rate for years, compounded times per year. A)
B)
C)
D)
E)
Question
Approximate the logarithm below using the properties of logarithms, given 
and 
A) -0.2084
B) 0.2625
C) -0.4709
D) -0.2625
E) 0.4709
and A) -0.2084
B) 0.2625
C) -0.4709
D) -0.2625
E) 0.4709
Question
Find the exact value of 
without using a calculator.
A)
B)
C)
D)
E) -1
without using a calculator.A)
B)
C)
D)
E) -1
Question
Evaluate the logarithm 
using the change of base formula.Round to 3 decimal places.
A) 6.303
B) 0.309
C) 3.239
D) 12.264
E) 2.737
using the change of base formula.Round to 3 decimal places.A) 6.303
B) 0.309
C) 3.239
D) 12.264
E) 2.737
Question
Condense the expression 
to the logarithm of a single term.
A)
B)
C)
D)
E)
to the logarithm of a single term.A)
B)
C)
D)
E)
Question
Use the properties of logarithms to simplify the logarithmic expression below. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Expand the given logarithmic expression.Assume all variable expressions represent positive real numbers. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
The demand function for a home theater system is given by 
a)Find the price p for a demand of x=200 units. b)Find the price p for a demand of x=900 units.
C)Use a graphing utility to graph the demand function.
D)Use the graph from part (c) to approximate the demand when the price is $400.
A) a)$435.23.
B)$45.78.
C)
D)$320.9
B) a)$545.26.
B)$71.32.
C)
D)$310.16
C) a)$573.26.
B)$34.98.
C)
D)$450.00
D) a)$345
B)$49.90.
C)
D)$542.00
E) a)$465.56.
B)$65.89.
C)
D)$359.78
a)Find the price p for a demand of x=200 units. b)Find the price p for a demand of x=900 units.C)Use a graphing utility to graph the demand function.
D)Use the graph from part (c) to approximate the demand when the price is $400.
A) a)$435.23.
B)$45.78.
C)
D)$320.9
B) a)$545.26.
B)$71.32.
C)
D)$310.16
C) a)$573.26.
B)$34.98.
C)
D)$450.00
D) a)$345
B)$49.90.
C)
D)$542.00
E) a)$465.56.
B)$65.89.
C)
D)$359.78
Question
You deposit a lump sum 
in a trust fund on the day your child is born.The fund earns 6.5% interest compounded continuously.Find the amount 
that will yield the given balance 
on your child's 25th birthday. 
A)
B)
C)
D)
E)
in a trust fund on the day your child is born.The fund earns 6.5% interest compounded continuously.Find the amount that will yield the given balance on your child's 25th birthday. A)
B)
C)
D)
E)
Question
Condense the expression 
to the logarithm of a single term.
A)
B)
C)
D)
E)
to the logarithm of a single term.A)
B)
C)
D)
E)
Question
The number of certain type of bacteria increases according to the model 
where t is time (in hours) a)Find P(0).
B)Find P(5).
C)Find P(10).
D)Find P(24).
A) a)
B)
C)
D)
B) a)
B)
C)
D)
C) a)
B)
C)
D)
D) a)
B)
C)
D)
E) a)
B)
C)
D)
where t is time (in hours) a)Find P(0).B)Find P(5).
C)Find P(10).
D)Find P(24).
A) a)
B)
C)
D)
B) a)
B)
C)
D)
C) a)
B)
C)
D)
D) a)
B)
C)
D)
E) a)
B)
C)
D)
Question
Write the expression below as a single logarithm with a coefficient of 1.Assume all variable expressions represent positive real numbers. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
The present value of money is the principal 
you need to invest today so that it will grow to an amount 
at the end of specified time.The present value formula 
is obtained by solving the compound interest formula 
for 
Recall that 
is the number of years, 
is the interest rate per year, and 
is the number of compoundings per year.find the present value of amount 
invested at rate 
for 
years, compounded 
times per year. 
A)
B)
C)
D)
E)
you need to invest today so that it will grow to an amount at the end of specified time.The present value formula is obtained by solving the compound interest formula for Recall that is the number of years, is the interest rate per year, and is the number of compoundings per year.find the present value of amount invested at rate for years, compounded times per year. A)
B)
C)
D)
E)
Question
Strontinum-90 has a half life of 29.1 years.The amount S of 100 kilograms of Strontinum6990 present after t years is given by 
How much of the 100 kilograms will remain after 50 years?
A) about 31.4 kilograms
B) about 35.4 kilograms
C) about 30.4 kilograms
D) about 37.4 kilograms
E) about 40.4 kilograms
How much of the 100 kilograms will remain after 50 years?A) about 31.4 kilograms
B) about 35.4 kilograms
C) about 30.4 kilograms
D) about 37.4 kilograms
E) about 40.4 kilograms
Question
The approximate lengths and diameters (in inches) of common nails are shown in the table.Find a logarithmic equation that relates the diameter 
of a common nail to its length 
A)
B)
C)
D)
E)
of a common nail to its length A)
B)
C)
D)
E)
Question
Determine whether 
Justify your answer.
A) Yes,
because 
is a rational number.
B) No,
because 
is not a rational number.
Justify your answer.A) Yes,
because is a rational number.B) No,
because is not a rational number. Question
The U.S.annual gross domestic product G (in billions of dollars) from 1985 through 2009 can be modeled by 
where 
represents the year, with 
corresponding to 1985 (Source: U.S.Bureau of Economics Analysis) (a) Use a graphing utility to graph G for the years 1985 through 2009.
(b) Use the graph from part (a) to estimate the gross domestic product in 1990,2000 and 2009.
A) a.
B) 1990: $5682.8 billion
2000: $4624.6 billion
2009: $15,463.8 billion
B) a.
B) 1990: $5682.8 billion
2000: $9624.6 billion
2009: $10,463.8 billion
C) a.
B) 1990: $5682.8 billion
2000: $9624.6 billion
2009: $15,463.8 billion
D) a.
B) 1990: $682.8 billion
2000: $9624.6 billion
2009: $15,463.8 billion
E) a.
B) 1990: $5682.8 billion
2000: $624.6 billion
2009: $15,463.8 billion
where represents the year, with corresponding to 1985 (Source: U.S.Bureau of Economics Analysis) (a) Use a graphing utility to graph G for the years 1985 through 2009.(b) Use the graph from part (a) to estimate the gross domestic product in 1990,2000 and 2009.
A) a.
B) 1990: $5682.8 billion
2000: $4624.6 billion
2009: $15,463.8 billion
B) a.
B) 1990: $5682.8 billion
2000: $9624.6 billion
2009: $10,463.8 billion
C) a.
B) 1990: $5682.8 billion
2000: $9624.6 billion
2009: $15,463.8 billion
D) a.
B) 1990: $682.8 billion
2000: $9624.6 billion
2009: $15,463.8 billion
E) a.
B) 1990: $5682.8 billion
2000: $624.6 billion
2009: $15,463.8 billion
Question
The average monthly sales 
(in billions of dollars) in retail trade in the United States from 1996 to 2005 can be approximated by the model 
where 
represents the year, with 
corresponding to 1996.Estimate the year in which the average monthly sales first exceeded $330 billion.
A) 2003
B) 2004
C) 2002
D) 1999
E) 1997
(in billions of dollars) in retail trade in the United States from 1996 to 2005 can be approximated by the model where represents the year, with corresponding to 1996.Estimate the year in which the average monthly sales first exceeded $330 billion.A) 2003
B) 2004
C) 2002
D) 1999
E) 1997
Question
Question
Solve for x: 
Round to 3 decimal places.
A) 1.407
B) 0.407
C) 1.362
D) -1.362
E) no solution
Round to 3 decimal places.A) 1.407
B) 0.407
C) 1.362
D) -1.362
E) no solution
Question
Question
Approximate the solution to 
Round to 3 decimal places.
A) -0.632
B) 0.500
C) 0.582
D) 2.718
E) 0.111
Round to 3 decimal places.A) -0.632
B) 0.500
C) 0.582
D) 2.718
E) 0.111
Question
Solve for x: 
Round to 3 decimal places.
A) 9.803
B) 15.777
C) 20.606
D) -20.606
E) -3.268
Round to 3 decimal places.A) 9.803
B) 15.777
C) 20.606
D) -20.606
E) -3.268
Question
Solve for 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use algebraic procedures to find the exact solution of the equation 
A) 0, -2
B) 4
C) 3, 2
D) -2, 4
E) 2
A) 0, -2
B) 4
C) 3, 2
D) -2, 4
E) 2
Question
Approximate the solution of 
to 3 decimal places.(You may use a graphing utility.)
A) -3.329
B) -0.299
C) -1.427
D) -0.986
E) -0.110
to 3 decimal places.(You may use a graphing utility.)A) -3.329
B) -0.299
C) -1.427
D) -0.986
E) -0.110
Question
Use algebraic procedures to find the exact solution(s) of the equation below. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Apply the Inverse Property of logarithmic or exponential functions to simplify the expression below. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Solve 
for x.
A) 1
B)
C)
D)
E) no solution
for x.A) 1
B)
C)
D)
E) no solution
Question
Use algebraic procedures to find the exact solution(s) of the equation below. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
An industrial psychologist has determined that the average percent score for an employee on a test of the employee's knowledge of the company's product is given by 
where t is the number of weeks on the job and P is the percent score.Estimate (to the nearest week) the expected number of weeks of employment that are necessary for an employee to earn a 90% score on the test.
A) 5 weeks
B) 50 weeks
C) 29 weeks
D) 43 weeks
E) 25 weeks
where t is the number of weeks on the job and P is the percent score.Estimate (to the nearest week) the expected number of weeks of employment that are necessary for an employee to earn a 90% score on the test.A) 5 weeks
B) 50 weeks
C) 29 weeks
D) 43 weeks
E) 25 weeks
Question
Solve the exponential equation algebraically.Approximate the result to three decimal places. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use a graphing utility to approximate the solution to 
Round to 3 decimal places.
A) 3.702
B) 2.702
C) 1.851
D) 1.351
E) no solution
Round to 3 decimal places.A) 3.702
B) 2.702
C) 1.851
D) 1.351
E) no solution
Question
Use algebraic procedures to find the exact solution of the equation 
A) -1, 7
B)
C) 2, 3
D) 7
E) 1
A) -1, 7
B)
C) 2, 3
D) 7
E) 1
Question
Question
Approximate the solution to 
Round to 3 decimal places.
A) 2.226
B) 6.133
C) 4.586
D) -0.223
E) 396.223
Round to 3 decimal places.A) 2.226
B) 6.133
C) 4.586
D) -0.223
E) 396.223
Question
Solve the exponential equation algebraically.Approximate the result to three decimal places. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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Deck 4: Exponential and Logarithmic Functions
1
Determine whether the function has an inverse function, If it does, find its inverse function.
A) No, does not have an inverse function.
B) Yes, has an inverse function,
C) Yes, has an inverse function,
D) Yes, has an inverse function,
E) Yes, has an inverse function,
A) No,
does not have an inverse function.B) Yes,
has an inverse function, C) Yes,
has an inverse function, D) Yes,
has an inverse function, E) Yes,
has an inverse function, A
2
The demand function for a limited edition comic book is given by Find the price for a demand of units.
A) $5789.56
B) $258.96
C) $312.99
D) $6312.99
E) $210.44
Find the price for a demand of units.A) $5789.56
B) $258.96
C) $312.99
D) $6312.99
E) $210.44
B
3
Evaluate the expression below.Round your results to three decimal places.
A) 0.135
B) 0.018
C) 54.598
D) 0.050
E) 0.007
A) 0.135
B) 0.018
C) 54.598
D) 0.050
E) 0.007
B
4
Determine whether the function has an inverse function, If it does, find its inverse function.
A) No, does not have an inverse function.
B) Yes, has an inverse function,
C) Yes, has an inverse function,
D) Yes, has an inverse function,
E) Yes, has an inverse function,
A) No,
does not have an inverse function.B) Yes,
has an inverse function, C) Yes,
has an inverse function, D) Yes,
has an inverse function, E) Yes,
has an inverse function, Unlock Deck
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5
Use the functions given by and to find the composition of functions
A)
B)
C)
D)
E)
and to find the composition of functions A)
B)
C)
D)
E)
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k this deck
6
Use the graph of to determine whether the function has an inverse function.
A) Yes, has an inverse function.
B) No, does not have an inverse function.
to determine whether the function has an inverse function. A) Yes,
has an inverse function.B) No,
does not have an inverse function. Unlock Deck
Unlock for access to all 92 flashcards in this deck.
Unlock Deck
k this deck
7
A company's profit for producing units is given by Find the inverse function and explain what it represents.Describe the domains of and
A) , represents the number of units that must be sold to obtain the profit of Domain of , Domain of
B) , represents the number of units that must be sold to obtain the profit of Domain of , Domain of
C) , represents the number of units that must be sold to obtain the profit of Domain of , Domain of
D) , represents the number of units that must be sold to obtain the profit of Domain of , Domain of
E) , represents the number of units that must be sold to obtain the profit of Domain of , Domain of
for producing units is given by Find the inverse function and explain what it represents.Describe the domains of and A)
, represents the number of units that must be sold to obtain the profit of Domain of , Domain of B)
, represents the number of units that must be sold to obtain the profit of Domain of , Domain of C)
, represents the number of units that must be sold to obtain the profit of Domain of , Domain of D)
, represents the number of units that must be sold to obtain the profit of Domain of , Domain of E)
, represents the number of units that must be sold to obtain the profit of Domain of , Domain of Unlock Deck
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8
Use the functions given by and to find the value
A) 1
B) 0
C) 3
D) 4
E) 2
and to find the value A) 1
B) 0
C) 3
D) 4
E) 2
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9
Sketch the graph of the function
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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Unlock Deck
k this deck
10
Use the graph of to determine whether the function has an inverse function.
A) No, does not have an inverse function.
B) Yes, has an inverse function.
to determine whether the function has an inverse function. A) No,
does not have an inverse function.B) Yes,
has an inverse function. Unlock Deck
Unlock for access to all 92 flashcards in this deck.
Unlock Deck
k this deck
11
Use the functions given by and to find the value
A) 16
B) -16
C) 32
D) The value does not exist.
E) -32
and to find the value A) 16
B) -16
C) 32
D) The value does not exist.
E) -32
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k this deck
12
Find the inverse function informally Verify that and
A) , ,
B) , ,
C) , ,
D) , ,
E) , ,
Verify that and A)
, , B)
, , C)
, , D)
, , E)
, , Unlock Deck
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k this deck
13
Use the functions given by and to find the composition of functions
A)
B)
C)
D)
E)
and to find the composition of functions A)
B)
C)
D)
E)
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k this deck
14
Use the functions given by and to find the value
A) 32
B) 35
C) 33
D) 37
E) 30
and to find the value A) 32
B) 35
C) 33
D) 37
E) 30
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k this deck
15
Show that and are functions by using the definition of inverse functions.
A)
B)
C)
D)
E)
and are functions by using the definition of inverse functions. A)
B)
C)
D)
E)
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k this deck
16
Show that and are functions by using the definition of inverse functions.
A)
B)
C)
D)
E)
and are functions by using the definition of inverse functions. A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 92 flashcards in this deck.
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k this deck
17
Find the inverse function of the function f given by the set of ordered pairs.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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k this deck
18
Determine which of the following functions is graphed below.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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k this deck
19
Find the inverse function informally Verify that and
A) , ,
B) , ,
C) , ,
D) , ,
E) , ,
Verify that and A)
, , B)
, , C)
, , D)
, , E)
, , Unlock Deck
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k this deck
20
Find the inverse function of the function f given by the set of ordered pairs.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 92 flashcards in this deck.
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k this deck
21
Sketch the graph of the function
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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Unlock Deck
k this deck
22
Write the logarithmic equation in its exponential form.
A)
B)
C)
D)
E)
in its exponential form.A)
B)
C)
D)
E)
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k this deck
23
Match the function with its graph.
A)
B)
C)
D)
E)
with its graph.A)
B)
C)
D)
E)
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k this deck
24
Find the vertical asymptote of the logarithmic function below.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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k this deck
25
Evaluate the logarithm without using a calculator.
A)
B)
C)
D)
E)
without using a calculator.A)
B)
C)
D)
E)
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k this deck
26
Use a calculator to evaluate Round your result to three decimal places.
A)
B)
C)
D)
E)
Round your result to three decimal places.A)
B)
C)
D)
E)
Unlock Deck
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k this deck
27
Sketch the graph of the function
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 92 flashcards in this deck.
Unlock Deck
k this deck
28
Match the function below with its graph. Graph I : Graph IV: Graph II: Graph V: Graph III:
A) Graph II
B) Graph V
C) Graph I
D) Graph IV
E) Graph III
Graph I : Graph IV: Graph II: Graph V: Graph III: A) Graph II
B) Graph V
C) Graph I
D) Graph IV
E) Graph III
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29
Sketch the graph of the function
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 92 flashcards in this deck.
Unlock Deck
k this deck
30
Use a calculator to evaluate Round your result to three decimal places.
A)
B)
C)
D)
E)
Round your result to three decimal places.A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 92 flashcards in this deck.
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k this deck
31
Rewrite the logarithmic equation in exponential form.
A)
B)
C)
D)
E)
in exponential form.A)
B)
C)
D)
E)
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k this deck
32
Use a calculator to evaluate the function for the given value of , Round your result to three decimal places.
A)
B)
C)
D)
E)
for the given value of , Round your result to three decimal places.A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 92 flashcards in this deck.
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k this deck
33
Use a calculator to evaluate the function for the given value of , Round your result to three decimal places.
A)
B)
C)
D)
E)
for the given value of , Round your result to three decimal places.A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 92 flashcards in this deck.
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k this deck
34
Write the logarithmic equation in exponential form.
A)
B)
C)
D)
E)
in exponential form.A)
B)
C)
D)
E)
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k this deck
35
Sketch the graph of the function
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 92 flashcards in this deck.
Unlock Deck
k this deck
36
Rewrite the exponential equation in logarithmic form.
A)
B)
C)
D)
E)
in logarithmic form.A)
B)
C)
D)
E)
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k this deck
37
Find the domain of the function
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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38
Write the exponential equation in its logarithmic form.
A)
B)
C)
D)
E)
in its logarithmic form.A)
B)
C)
D)
E)
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k this deck
39
Write the exponential equation in logarithmic form.
A)
B)
C)
D)
E)
in logarithmic form.A)
B)
C)
D)
E)
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k this deck
40
Match the function with its graph.
A)
B)
C)
D)
E)
with its graph.A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 92 flashcards in this deck.
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k this deck
41
Write as a single logarithm with a coefficient of 1. Assume all variable expressions represent positive real numbers.
A)
B)
C)
D)
E)
as a single logarithm with a coefficient of 1. Assume all variable expressions represent positive real numbers.A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 92 flashcards in this deck.
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k this deck
42
Expand the logarithmic expression Assume all variable expressions represent positive real numbers.
A)
B)
C)
D)
E)
Assume all variable expressions represent positive real numbers.A)
B)
C)
D)
E)
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43
Solve for x.
A)
B)
C)
D)
E) 2
A)
B)
C)
D)
E) 2
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k this deck
44
The present value of money is the principal you need to invest today so that it will grow to an amount at the end of specified time.The present value formula is obtained by solving the compound interest formula for Recall that is the number of years, is the interest rate per year, and is the number of compoundings per year.find the present value of amount invested at rate for years, compounded times per year.
A)
B)
C)
D)
E)
you need to invest today so that it will grow to an amount at the end of specified time.The present value formula is obtained by solving the compound interest formula for Recall that is the number of years, is the interest rate per year, and is the number of compoundings per year.find the present value of amount invested at rate for years, compounded times per year. A)
B)
C)
D)
E)
Unlock Deck
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k this deck
45
Approximate the logarithm below using the properties of logarithms, given and
A) -0.2084
B) 0.2625
C) -0.4709
D) -0.2625
E) 0.4709
and A) -0.2084
B) 0.2625
C) -0.4709
D) -0.2625
E) 0.4709
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k this deck
46
Find the exact value of without using a calculator.
A)
B)
C)
D)
E) -1
without using a calculator.A)
B)
C)
D)
E) -1
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k this deck
47
Evaluate the logarithm using the change of base formula.Round to 3 decimal places.
A) 6.303
B) 0.309
C) 3.239
D) 12.264
E) 2.737
using the change of base formula.Round to 3 decimal places.A) 6.303
B) 0.309
C) 3.239
D) 12.264
E) 2.737
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k this deck
48
Condense the expression to the logarithm of a single term.
A)
B)
C)
D)
E)
to the logarithm of a single term.A)
B)
C)
D)
E)
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k this deck
49
Use the properties of logarithms to simplify the logarithmic expression below.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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k this deck
50
Expand the given logarithmic expression.Assume all variable expressions represent positive real numbers.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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k this deck
51
The demand function for a home theater system is given by a)Find the price p for a demand of x=200 units. b)Find the price p for a demand of x=900 units.
C)Use a graphing utility to graph the demand function.
D)Use the graph from part (c) to approximate the demand when the price is $400.
A) a)$435.23.
B)$45.78.
C)
D)$320.9
B) a)$545.26.
B)$71.32.
C)
D)$310.16
C) a)$573.26.
B)$34.98.
C)
D)$450.00
D) a)$345
B)$49.90.
C)
D)$542.00
E) a)$465.56.
B)$65.89.
C)
D)$359.78
a)Find the price p for a demand of x=200 units. b)Find the price p for a demand of x=900 units.C)Use a graphing utility to graph the demand function.
D)Use the graph from part (c) to approximate the demand when the price is $400.
A) a)$435.23.
B)$45.78.
C)
D)$320.9
B) a)$545.26.
B)$71.32.
C)
D)$310.16
C) a)$573.26.
B)$34.98.
C)
D)$450.00
D) a)$345
B)$49.90.
C)
D)$542.00
E) a)$465.56.
B)$65.89.
C)
D)$359.78
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k this deck
52
You deposit a lump sum in a trust fund on the day your child is born.The fund earns 6.5% interest compounded continuously.Find the amount that will yield the given balance on your child's 25th birthday.
A)
B)
C)
D)
E)
in a trust fund on the day your child is born.The fund earns 6.5% interest compounded continuously.Find the amount that will yield the given balance on your child's 25th birthday. A)
B)
C)
D)
E)
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k this deck
53
Condense the expression to the logarithm of a single term.
A)
B)
C)
D)
E)
to the logarithm of a single term.A)
B)
C)
D)
E)
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k this deck
54
The number of certain type of bacteria increases according to the model where t is time (in hours) a)Find P(0).
B)Find P(5).
C)Find P(10).
D)Find P(24).
A) a)
B)
C)
D)
B) a)
B)
C)
D)
C) a)
B)
C)
D)
D) a)
B)
C)
D)
E) a)
B)
C)
D)
where t is time (in hours) a)Find P(0).B)Find P(5).
C)Find P(10).
D)Find P(24).
A) a)
B)
C)
D)
B) a)
B)
C)
D)
C) a)
B)
C)
D)
D) a)
B)
C)
D)
E) a)
B)
C)
D)
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55
Write the expression below as a single logarithm with a coefficient of 1.Assume all variable expressions represent positive real numbers.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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56
The present value of money is the principal you need to invest today so that it will grow to an amount at the end of specified time.The present value formula is obtained by solving the compound interest formula for Recall that is the number of years, is the interest rate per year, and is the number of compoundings per year.find the present value of amount invested at rate for years, compounded times per year.
A)
B)
C)
D)
E)
you need to invest today so that it will grow to an amount at the end of specified time.The present value formula is obtained by solving the compound interest formula for Recall that is the number of years, is the interest rate per year, and is the number of compoundings per year.find the present value of amount invested at rate for years, compounded times per year. A)
B)
C)
D)
E)
Unlock Deck
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57
Strontinum-90 has a half life of 29.1 years.The amount S of 100 kilograms of Strontinum6990 present after t years is given by How much of the 100 kilograms will remain after 50 years?
A) about 31.4 kilograms
B) about 35.4 kilograms
C) about 30.4 kilograms
D) about 37.4 kilograms
E) about 40.4 kilograms
How much of the 100 kilograms will remain after 50 years?A) about 31.4 kilograms
B) about 35.4 kilograms
C) about 30.4 kilograms
D) about 37.4 kilograms
E) about 40.4 kilograms
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k this deck
58
The approximate lengths and diameters (in inches) of common nails are shown in the table.Find a logarithmic equation that relates the diameter of a common nail to its length
A)
B)
C)
D)
E)
of a common nail to its length A)
B)
C)
D)
E)
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k this deck
59
Determine whether Justify your answer.
A) Yes, because is a rational number.
B) No, because is not a rational number.
Justify your answer.A) Yes,
because is a rational number.B) No,
because is not a rational number. Unlock Deck
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k this deck
60
The U.S.annual gross domestic product G (in billions of dollars) from 1985 through 2009 can be modeled by where represents the year, with corresponding to 1985 (Source: U.S.Bureau of Economics Analysis) (a) Use a graphing utility to graph G for the years 1985 through 2009.
(b) Use the graph from part (a) to estimate the gross domestic product in 1990,2000 and 2009.
A) a.
B) 1990: $5682.8 billion
2000: $4624.6 billion
2009: $15,463.8 billion
B) a.
B) 1990: $5682.8 billion
2000: $9624.6 billion
2009: $10,463.8 billion
C) a.
B) 1990: $5682.8 billion
2000: $9624.6 billion
2009: $15,463.8 billion
D) a.
B) 1990: $682.8 billion
2000: $9624.6 billion
2009: $15,463.8 billion
E) a.
B) 1990: $5682.8 billion
2000: $624.6 billion
2009: $15,463.8 billion
where represents the year, with corresponding to 1985 (Source: U.S.Bureau of Economics Analysis) (a) Use a graphing utility to graph G for the years 1985 through 2009.(b) Use the graph from part (a) to estimate the gross domestic product in 1990,2000 and 2009.
A) a.
B) 1990: $5682.8 billion
2000: $4624.6 billion
2009: $15,463.8 billion
B) a.
B) 1990: $5682.8 billion
2000: $9624.6 billion
2009: $10,463.8 billion
C) a.
B) 1990: $5682.8 billion
2000: $9624.6 billion
2009: $15,463.8 billion
D) a.
B) 1990: $682.8 billion
2000: $9624.6 billion
2009: $15,463.8 billion
E) a.
B) 1990: $5682.8 billion
2000: $624.6 billion
2009: $15,463.8 billion
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61
The average monthly sales (in billions of dollars) in retail trade in the United States from 1996 to 2005 can be approximated by the model where represents the year, with corresponding to 1996.Estimate the year in which the average monthly sales first exceeded $330 billion.
A) 2003
B) 2004
C) 2002
D) 1999
E) 1997
(in billions of dollars) in retail trade in the United States from 1996 to 2005 can be approximated by the model where represents the year, with corresponding to 1996.Estimate the year in which the average monthly sales first exceeded $330 billion.A) 2003
B) 2004
C) 2002
D) 1999
E) 1997
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k this deck
62
Find the balance if $27,000 is invested at an annual rate of 6.5% for 4 years, compounded continuously.
A) $115,253.17
B) $34,020.00
C) $28,798.24
D) $20,818.39
E) $35,017.11
A) $115,253.17
B) $34,020.00
C) $28,798.24
D) $20,818.39
E) $35,017.11
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k this deck
63
Solve for x: Round to 3 decimal places.
A) 1.407
B) 0.407
C) 1.362
D) -1.362
E) no solution
Round to 3 decimal places.A) 1.407
B) 0.407
C) 1.362
D) -1.362
E) no solution
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k this deck
64
An initial investment of $6000 grows at an annual interest rate of 3% compounded continuously.How long will it take to double the investment?
A) 23.10 years
B) 24.10 years
C) 24.00 years
D) 23.00 years
E) 1 year
A) 23.10 years
B) 24.10 years
C) 24.00 years
D) 23.00 years
E) 1 year
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k this deck
65
Approximate the solution to Round to 3 decimal places.
A) -0.632
B) 0.500
C) 0.582
D) 2.718
E) 0.111
Round to 3 decimal places.A) -0.632
B) 0.500
C) 0.582
D) 2.718
E) 0.111
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k this deck
66
Solve for x: Round to 3 decimal places.
A) 9.803
B) 15.777
C) 20.606
D) -20.606
E) -3.268
Round to 3 decimal places.A) 9.803
B) 15.777
C) 20.606
D) -20.606
E) -3.268
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67
Solve for
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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68
Use algebraic procedures to find the exact solution of the equation
A) 0, -2
B) 4
C) 3, 2
D) -2, 4
E) 2
A) 0, -2
B) 4
C) 3, 2
D) -2, 4
E) 2
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69
Approximate the solution of to 3 decimal places.(You may use a graphing utility.)
A) -3.329
B) -0.299
C) -1.427
D) -0.986
E) -0.110
to 3 decimal places.(You may use a graphing utility.)A) -3.329
B) -0.299
C) -1.427
D) -0.986
E) -0.110
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70
Use algebraic procedures to find the exact solution(s) of the equation below.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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71
Apply the Inverse Property of logarithmic or exponential functions to simplify the expression below.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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Unlock Deck
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72
Solve for x.
A) 1
B)
C)
D)
E) no solution
for x.A) 1
B)
C)
D)
E) no solution
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Unlock Deck
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73
Use algebraic procedures to find the exact solution(s) of the equation below.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 92 flashcards in this deck.
Unlock Deck
k this deck
74
An industrial psychologist has determined that the average percent score for an employee on a test of the employee's knowledge of the company's product is given by where t is the number of weeks on the job and P is the percent score.Estimate (to the nearest week) the expected number of weeks of employment that are necessary for an employee to earn a 90% score on the test.
A) 5 weeks
B) 50 weeks
C) 29 weeks
D) 43 weeks
E) 25 weeks
where t is the number of weeks on the job and P is the percent score.Estimate (to the nearest week) the expected number of weeks of employment that are necessary for an employee to earn a 90% score on the test.A) 5 weeks
B) 50 weeks
C) 29 weeks
D) 43 weeks
E) 25 weeks
Unlock Deck
Unlock for access to all 92 flashcards in this deck.
Unlock Deck
k this deck
75
Solve the exponential equation algebraically.Approximate the result to three decimal places.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 92 flashcards in this deck.
Unlock Deck
k this deck
76
Use a graphing utility to approximate the solution to Round to 3 decimal places.
A) 3.702
B) 2.702
C) 1.851
D) 1.351
E) no solution
Round to 3 decimal places.A) 3.702
B) 2.702
C) 1.851
D) 1.351
E) no solution
Unlock Deck
Unlock for access to all 92 flashcards in this deck.
Unlock Deck
k this deck
77
Use algebraic procedures to find the exact solution of the equation
A) -1, 7
B)
C) 2, 3
D) 7
E) 1
A) -1, 7
B)
C) 2, 3
D) 7
E) 1
Unlock Deck
Unlock for access to all 92 flashcards in this deck.
Unlock Deck
k this deck
78
How long will it take $10,000 to quadruple if it is invested in a savings account that pays 5.5% annual interest compounded continuously? Round to the nearest year.
A) 25 years
B) 20 years
C) 19 years
D) 32 years
E) 30 years
A) 25 years
B) 20 years
C) 19 years
D) 32 years
E) 30 years
Unlock Deck
Unlock for access to all 92 flashcards in this deck.
Unlock Deck
k this deck
79
Approximate the solution to Round to 3 decimal places.
A) 2.226
B) 6.133
C) 4.586
D) -0.223
E) 396.223
Round to 3 decimal places.A) 2.226
B) 6.133
C) 4.586
D) -0.223
E) 396.223
Unlock Deck
Unlock for access to all 92 flashcards in this deck.
Unlock Deck
k this deck
80
Solve the exponential equation algebraically.Approximate the result to three decimal places.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 92 flashcards in this deck.
Unlock Deck
k this deck
Unlock Deck
Unlock for access to all 92 flashcards in this deck.
