Question 1

Use the exponential decay formula with half-lives to find the final amount. Round to the nearest tenth when necessary.
-

Accepted Answer

A)  2025 
B)  75 
C)  189 
D)  300 
A)  2025 
B)  75 
C)  189 
D)  300

Question 2

Graph the function.
-$y = \log _ { 4 } x$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 3

Solve the equation for x. Give an exact solution.
-$\log ( 13 x + 3 ) = - 0.5$

Accepted Answer

A)  $13 \left( 10 ^ { - 0.5 } - 3 \right)$ 
B)  $\frac { 10 ^ { - 0.5 } + 13 } { 3 }$ 
C)  $\frac { 10 ^ { - 0.5 } - 3 } { 13 }$ 
D)  $10 ^ { - 0.5 } - 3$ 
A)  $13 \left( 10 ^ { - 0.5 } - 3 \right)$ 
B)  $\frac { 10 ^ { - 0.5 } + 13 } { 3 }$ 
C)  $\frac { 10 ^ { - 0.5 } - 3 } { 13 }$ 
D)  $10 ^ { - 0.5 } - 3$

Question 4

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

Accepted Answer

A) True 
 B)False

Question 5

Express as the logarithm of a single expression. Assume that variables represent positive numbers.
-$\log _ { 6 } 11 - \log _ { 6 } x$

Accepted Answer

A)  $\log _ { 6 } ( 11 - \mathrm { x } )$ 
B)  $\log _ { 6 } \frac { x } { 11 }$ 
C)  $\log _ { 6 } \frac { 11 } { x }$ 
D)  $\log _ { 12 } \frac { 11 } { x }$ 
A)  $\log _ { 6 } ( 11 - \mathrm { x } )$ 
B)  $\log _ { 6 } \frac { x } { 11 }$ 
C)  $\log _ { 6 } \frac { 11 } { x }$ 
D)  $\log _ { 12 } \frac { 11 } { x }$

Question 6

Solve.
-Business people are concerned with cost functions, revenue functions, and profit functions. Suppose the revenue $R ( x )$ for $x$ units of a product can be described by $R ( x ) = 400 x$, and the cost $C ( x )$ can be described by $C ( x ) = 2200 + 180 x$. Find the profit $P ( x )$ for $x$ units.

Accepted Answer

A)  $\mathrm { P } ( \mathrm { x } ) = 220 \mathrm { x } - 2200$ 
B)  $P ( x ) = \frac { 220 } { x } - 2200$ 
C)  $\mathrm { P } ( \mathrm { x } ) = 580 \mathrm { x } - 2200$ 
D)  $\mathrm { P } ( \mathrm { x } ) = 220 \mathrm { x } + 2200$ 
A)  $\mathrm { P } ( \mathrm { x } ) = 220 \mathrm { x } - 2200$ 
B)  $P ( x ) = \frac { 220 } { x } - 2200$ 
C)  $\mathrm { P } ( \mathrm { x } ) = 580 \mathrm { x } - 2200$ 
D)  $\mathrm { P } ( \mathrm { x } ) = 220 \mathrm { x } + 2200$

Question 7

For the given functions f and g, find the requested function.
-If $f ( x ) = 5 x + 9$ and $g ( x ) = 3 x - 1$, find $( f \cdot g ) ( x )$.

Accepted Answer

A)  $( f \cdot g ) ( x ) = 8 x ^ { 2 } + 22 x + 8$ 
B)  $( \mathrm { f } \cdot \mathrm { g } ) ( \mathrm { x } ) = 15 \mathrm { x } ^ { 2 } - 9$ 
C)  $( f \cdot g ) ( x ) = 15 x ^ { 2 } + 26 x - 9$ 
D)  $( f \cdot g ) ( x ) = 15 x ^ { 2 } + 22 x - 9$ 
A)  $( f \cdot g ) ( x ) = 8 x ^ { 2 } + 22 x + 8$ 
B)  $( \mathrm { f } \cdot \mathrm { g } ) ( \mathrm { x } ) = 15 \mathrm { x } ^ { 2 } - 9$ 
C)  $( f \cdot g ) ( x ) = 15 x ^ { 2 } + 26 x - 9$ 
D)  $( f \cdot g ) ( x ) = 15 x ^ { 2 } + 22 x - 9$

Question 8

Find the value of the logarithmic expression.
-$\log _ { 10 } \frac { 1 } { 10000 }$

Accepted Answer

A)  $- 40$ 
B)  4 
C)  $- 4$ 
D)  10,000 
A)  $- 40$ 
B)  4 
C)  $- 4$ 
D)  10,000

Question 9

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

Accepted Answer

A) True 
 B)False

Question 10

Solve.
-Calculate how much money Carlos has after 7 years if he originally invested $\$ 8400$ at $7.7 \%$ compounded continuously. Use $\mathrm { A } = \mathrm { Pe } ^ { \mathrm { rt } }$, where $\mathrm { A }$ is the final amount, $\mathrm { P }$ is the original amount deposited, $\mathrm { r }$ is the interest rate, and $\mathrm { t }$ is the number of years.

Accepted Answer

A)  $\$ 14,452.05$ 
B)  $\$ 14,345.05$ 
C)  $\$ 14,400.05$ 
D)  $\$ 1,230,729.27$ 
A)  $\$ 14,452.05$ 
B)  $\$ 14,345.05$ 
C)  $\$ 14,400.05$ 
D)  $\$ 1,230,729.27$

Question 11

Solve the equation. Give an exact solution.
-$3 ^ { x + 6 } = 2$

Accepted Answer

A)  $\frac { \log 2 } { \log 3 } - 6$ 
B)  $\frac { \log 3 } { \log 2 } + \log 6$ 
C)  $\log 2 - \log 3 - \log 6$ 
D)  $\frac { \log 3 } { \log 2 } + 6$ 
A)  $\frac { \log 2 } { \log 3 } - 6$ 
B)  $\frac { \log 3 } { \log 2 } + \log 6$ 
C)  $\log 2 - \log 3 - \log 6$ 
D)  $\frac { \log 3 } { \log 2 } + 6$

Question 12

Find the inverse of the one-to-one function.
-$f ( x ) = \frac { 5 x - 1 } { 4 }$

Accepted Answer

A)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 4 \mathrm { x } - 1 } { 5 }$ 
B)  $f ^ { - 1 } ( x ) = \frac { 4 } { 5 x - 1 }$ 
C)  $f ^ { - 1 } ( x ) = \frac { 4 x + 1 } { 5 }$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 4 } { 5 \mathrm { x } + 1 }$ 
A)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 4 \mathrm { x } - 1 } { 5 }$ 
B)  $f ^ { - 1 } ( x ) = \frac { 4 } { 5 x - 1 }$ 
C)  $f ^ { - 1 } ( x ) = \frac { 4 x + 1 } { 5 }$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 4 } { 5 \mathrm { x } + 1 }$

Question 13

Write the function F(x) as a composition of f, g, or h.
-$\begin{array} { l } 
f ( x ) = x ^ { 2 } - 6 \quad g ( x ) = - 5 x \quad h ( x ) = \sqrt { x + 5 } \
F ( x ) = - 5 x ^ { 2 } + 30
\end{array}$

Accepted Answer

A)  $F ( x ) = ( g \circ f ) ( x )$ 
B)  $F ( x ) = ( h \circ g ) ( x )$ 
C)  $F ( x ) = ( f \circ g ) ( x )$ 
D)  $F ( x ) = ( g \circ h ) ( x )$ 
A)  $F ( x ) = ( g \circ f ) ( x )$ 
B)  $F ( x ) = ( h \circ g ) ( x )$ 
C)  $F ( x ) = ( f \circ g ) ( x )$ 
D)  $F ( x ) = ( g \circ h ) ( x )$

Question 14

Provide an appropriate response.
-Approximate $\log _ { 2 } 5$ to four decimal places.

Accepted Answer

A)  $0.4307$ 
B)  $2.3219$ 
C)  $1.0000$ 
D)  $0.3979$ 
A)  $0.4307$ 
B)  $2.3219$ 
C)  $1.0000$ 
D)  $0.3979$

Question 15

Solve.
-The rabbit population in a forest area grows at the rate of $6 \%$ monthly. If there are 280 rabbits in September, find how many rabbits (rounded to the nearest whole number) should be expected by next September. Use $y = 280 ( 2.7 ) ^ { 0.06 t }$.

Accepted Answer

A)  559 rabbits 
B)  585 rabbits 
C)  544 rabbits 
D)  572 rabbits 
A)  559 rabbits 
B)  585 rabbits 
C)  544 rabbits 
D)  572 rabbits

Question 16

Write as an exponential equation.
-$\log _ { 3 } \frac { 1 } { 27 } = - 3$

Accepted Answer

A) $\left( \frac { 1 } { 27 } \right) ^ { - 3 }= 3$ 
B)  $3 ^ { 3 } = \frac { 1 } { 27 }$ 
C)  $3 ^ { - 3 } = \frac { 1 } { 27 }$ 
D)  $3 ^ { 27 } = 3$ 
A) $\left( \frac { 1 } { 27 } \right) ^ { - 3 }= 3$ 
B)  $3 ^ { 3 } = \frac { 1 } { 27 }$ 
C)  $3 ^ { - 3 } = \frac { 1 } { 27 }$ 
D)  $3 ^ { 27 } = 3$

Question 17

Find f(x) and g(x) so that the given function h(x) = (f ° g)(x).
-$h ( x ) = \left| 1 - 6 x ^ { 2 } \right|$

Accepted Answer

A)  $f ( x ) = 1 - 6 x ^ { 2 } ; g ( x ) = | x |$ 
B)  $f ( x ) = 1 - 6 x ^ { 2 } ; g ( x ) = \left| x ^ { 2 } \right|$ 
C)  $f ( x ) = | x | ; g ( x ) = 1 - 6 x$ 
D)  $f ( x ) = | x | ; g ( x ) = 1 - 6 x ^ { 2 }$ 
A)  $f ( x ) = 1 - 6 x ^ { 2 } ; g ( x ) = | x |$ 
B)  $f ( x ) = 1 - 6 x ^ { 2 } ; g ( x ) = \left| x ^ { 2 } \right|$ 
C)  $f ( x ) = | x | ; g ( x ) = 1 - 6 x$ 
D)  $f ( x ) = | x | ; g ( x ) = 1 - 6 x ^ { 2 }$

Question 18

Solve. Round the answer to the nearest whole number.
-Suppose a city with population 340,000 has been growing at a rate of $5 \%$ per year. If this rate continues, find the population of this city in 20 years.

Accepted Answer

A)  744,982 
B)  846,029 
C)  $1,090,426$ 
D)  902,121 
A)  744,982 
B)  846,029 
C)  $1,090,426$ 
D)  902,121

Question 19

The graph of an exponential function is given. Match the graph to one of the following functions.
-

Accepted Answer

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

Question 20

Fill in the blank with one of the words or phrases listed below. Some words or phrases may be used more than once. $$\begin{array} { l l l l } 
\text { inverse } & \text { common } & \text { composition symmetric } & \text { exponential } \
\text { vertical } & \text { logarithmic } & \text { natural } \quad \text { half-life } & \text { horizontal }
\end{array}$$
-A function of the form $f ( x ) = b ^ { x }$ is called $a ( n )$______ function if $b > 0$, $b$ is not 1 , and $x$ is a real number.

Accepted Answer

A)  symmetric 
B)  inverse 
C)  logarithmic 
D)  exponential 
A)  symmetric 
B)  inverse 
C)  logarithmic 
D)  exponential

Use the exponential decay formula with half-lives to find the final amount. Round to the nearest tenth when necessary. -

Graph the function. - $y = \log _ { 4 } x$ $Graph the function. - y = \log _ { 4 } x$

Solve the equation for x. Give an exact solution. - $\log ( 13 x + 3 ) = - 0.5$

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

Express as the logarithm of a single expression. Assume that variables represent positive numbers. - $\log _ { 6 } 11 - \log _ { 6 } x$

For the given functions f and g, find the requested function. -If $f ( x ) = 5 x + 9$ and $g ( x ) = 3 x - 1$ , find $( f \cdot g ) ( x )$ .

Find the value of the logarithmic expression. - $\log _ { 10 } \frac { 1 } { 10000 }$

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

Solve the equation. Give an exact solution. - $3 ^ { x + 6 } = 2$

Find the inverse of the one-to-one function. - $f ( x ) = \frac { 5 x - 1 } { 4 }$

Write the function F(x) as a composition of f, g, or h. - f(x)=-6g(x)=-5xh(x)= F(x)=-5+30

Provide an appropriate response. -Approximate $\log _ { 2 } 5$ to four decimal places.

Solve. -The rabbit population in a forest area grows at the rate of $6 \%$ monthly. If there are 280 rabbits in September, find how many rabbits (rounded to the nearest whole number) should be expected by next September. Use $y = 280 ( 2.7 ) ^ { 0.06 t }$ .

Write as an exponential equation. - $\log _ { 3 } \frac { 1 } { 27 } = - 3$

Find f(x) and g(x) so that the given function h(x) = (f ° g)(x). - $h ( x ) = \left| 1 - 6 x ^ { 2 } \right|$

Solve. Round the answer to the nearest whole number. -Suppose a city with population 340,000 has been growing at a rate of $5 \%$ per year. If this rate continues, find the population of this city in 20 years.

The graph of an exponential function is given. Match the graph to one of the following functions. -

Review of Real Numbers

Equations, Inequalities, and Problem Solving

Graphing

Solving Systems of Linear Equations

Exponents and Polynomials

Factoring Polynomials

Rational Expressions

More on Functions and Graphs

Inequalities and Absolute Value

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 12: Exponential and Logarithmic Functions

Use the exponential decay formula with half-lives to find the final amount. Round to the nearest tenth when necessary. -

Graph the function. - y=log⁡4xy = \log _ { 4 } xy=log4​x

Solve the equation for x. Give an exact solution. - log⁡(13x+3)=−0.5\log ( 13 x + 3 ) = - 0.5log(13x+3)=−0.5

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

Express as the logarithm of a single expression. Assume that variables represent positive numbers. - log⁡611−log⁡6x\log _ { 6 } 11 - \log _ { 6 } xlog6​11−log6​x

For the given functions f and g, find the requested function. -If f(x)=5x+9f ( x ) = 5 x + 9f(x)=5x+9 and g(x)=3x−1g ( x ) = 3 x - 1g(x)=3x−1 , find (f⋅g)(x)( f \cdot g ) ( x )(f⋅g)(x) .

Find the value of the logarithmic expression. - log⁡10110000\log _ { 10 } \frac { 1 } { 10000 }log10​100001​

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

Solve the equation. Give an exact solution. - 3x+6=23 ^ { x + 6 } = 23x+6=2

Find the inverse of the one-to-one function. - f(x)=5x−14f ( x ) = \frac { 5 x - 1 } { 4 }f(x)=45x−1​

Write the function F(x) as a composition of f, g, or h. - f(x)=-6g(x)=-5xh(x)= F(x)=-5+30

Provide an appropriate response. -Approximate log⁡25\log _ { 2 } 5log2​5 to four decimal places.

Solve. -The rabbit population in a forest area grows at the rate of 6%6 \%6% monthly. If there are 280 rabbits in September, find how many rabbits (rounded to the nearest whole number) should be expected by next September. Use y=280(2.7)0.06ty = 280 ( 2.7 ) ^ { 0.06 t }y=280(2.7)0.06t .

Write as an exponential equation. - log⁡3127=−3\log _ { 3 } \frac { 1 } { 27 } = - 3log3​271​=−3

Find f(x) and g(x) so that the given function h(x) = (f ° g)(x). - h(x)=∣1−6x2∣h ( x ) = \left| 1 - 6 x ^ { 2 } \right|h(x)=​1−6x2​

Solve. Round the answer to the nearest whole number. -Suppose a city with population 340,000 has been growing at a rate of 5%5 \%5% per year. If this rate continues, find the population of this city in 20 years.

The graph of an exponential function is given. Match the graph to one of the following functions. -

Review of Real Numbers

Equations, Inequalities, and Problem Solving

Graphing

Solving Systems of Linear Equations

Exponents and Polynomials

Factoring Polynomials

Rational Expressions

More on Functions and Graphs

Inequalities and Absolute Value

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Graph the function. - $y = \log _ { 4 } x$ $Graph the function. - y = \log _ { 4 } x$

Solve the equation for x. Give an exact solution. - $\log ( 13 x + 3 ) = - 0.5$

Express as the logarithm of a single expression. Assume that variables represent positive numbers. - $\log _ { 6 } 11 - \log _ { 6 } x$

For the given functions f and g, find the requested function. -If $f ( x ) = 5 x + 9$ and $g ( x ) = 3 x - 1$ , find $( f \cdot g ) ( x )$ .

Find the value of the logarithmic expression. - $\log _ { 10 } \frac { 1 } { 10000 }$

Solve the equation. Give an exact solution. - $3 ^ { x + 6 } = 2$

Find the inverse of the one-to-one function. - $f ( x ) = \frac { 5 x - 1 } { 4 }$

Provide an appropriate response. -Approximate $\log _ { 2 } 5$ to four decimal places.

Solve. -The rabbit population in a forest area grows at the rate of $6 \%$ monthly. If there are 280 rabbits in September, find how many rabbits (rounded to the nearest whole number) should be expected by next September. Use $y = 280 ( 2.7 ) ^ { 0.06 t }$ .

Write as an exponential equation. - $\log _ { 3 } \frac { 1 } { 27 } = - 3$

Find f(x) and g(x) so that the given function h(x) = (f ° g)(x). - $h ( x ) = \left| 1 - 6 x ^ { 2 } \right|$

Solve. Round the answer to the nearest whole number. -Suppose a city with population 340,000 has been growing at a rate of $5 \%$ per year. If this rate continues, find the population of this city in 20 years.