Question 1

Decide whether the statement is true or false.
-$$\log _ { 8 } 384 - \log _ { 8 } 48 = 1$$

Accepted Answer

A)  False 
B)  True 
A)  False 
B)  True

Question 2

Solve the logarithmic equation. Give an exact solution.
-$$\log _ { 3 } ( x + 6 ) - \log _ { 3 } ( x - 3 ) = 3$$

Accepted Answer

A)  $\left\{ \frac { 87 } { 26 } \right\}$ 
B)  $\{ 18 \}$ 
C)  $\left\{ \frac { 33 } { 8 } \right\}$ 
D)  $\left\{ \frac { 9 } { 26 } \right\}$ 
A)  $\left\{ \frac { 87 } { 26 } \right\}$ 
B)  $\{ 18 \}$ 
C)  $\left\{ \frac { 33 } { 8 } \right\}$ 
D)  $\left\{ \frac { 9 } { 26 } \right\}$

Question 3

Use the exponential decay formula with half-lives to find the final amount. Round to the nearest tenth when necessary.
-$\begin{array}{c|c|c|c}
\begin{array}{c}
\text { Original } \
\text { Amount }
\end{array} & \begin{array}{c}
\text { Half-Life } \
\text { (in years) }
\end{array} & \begin{array}{c}
\text { Number } \
\text { of Years }
\end{array} & \begin{array}{c}
\text { Final Amount after } \
\text { x Time Intervals }
\end{array} \
\hline 26 & 125 & 800 &
\end{array}$

Accepted Answer

A)  $2.8$ 
B)  0 
C)  $0.3$ 
D)  $0.4$ 
A)  $2.8$ 
B)  0 
C)  $0.3$ 
D)  $0.4$

Question 4

Fill in the blank with one of the words or phrases listed below. Some words or phrases may be used more than once. $$\begin{array} { l l l l } 
\text { inverse } & \text { common } & \text { composition symmetric } & \text { exponential } \
\text { vertical } & \text { logarithmic } & \text { natural half-life } & \text { horizontal }
\end{array}$$
-To see whether a graph is the graph of a one-to-one function, apply the line test to see whether it is a function, and then apply the line test to see whether it is a one-to-one function.

Accepted Answer

A)  horizontal; inverse 
B)  vertical; exponential 
C)  vertical; horizontal 
D)  horizontal; vertical 
A)  horizontal; inverse 
B)  vertical; exponential 
C)  vertical; horizontal 
D)  horizontal; vertical

Question 5

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

Accepted Answer

A)  Yes 
B)  No 
A)  Yes 
B)  No

Question 6

Graph the function.
-$f ( x ) = e ^ { 6 x }$

Accepted Answer

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

Question 7

Express as the logarithm of a single expression. Assume that variables represent positive numbers.
-$\log _ { \mathrm { b } } \mathrm { u } + \log _ { \mathrm { b } } \mathrm { v }$

Accepted Answer

A)  $\log _ { 2 b }$ uv 
B)  $\log _ { b } u v$ 
C)  $\log _ { b } ( u + v )$ 
D)  $\log _ { \mathrm { b } } \frac { \mathrm { u } } { \mathrm { v } }$ 
A)  $\log _ { 2 b }$ uv 
B)  $\log _ { b } u v$ 
C)  $\log _ { b } ( u + v )$ 
D)  $\log _ { \mathrm { b } } \frac { \mathrm { u } } { \mathrm { v } }$

Question 8

Write as an exponential equation.
-$$\log _ { 3 } \sqrt { 3 } = \frac { 1 } { 2 }$$

Accepted Answer

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

Question 9

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

Accepted Answer

A)  Yes 
B)  No 
A)  Yes 
B)  No

Question 10

Solve the equation. Give an exact solution.
-$$3 ^ { x + 8 } = 7$$

Accepted Answer

A)  $\{ \log 7 - \log 3 - \log 8 \}$ 
B)  $\left\{ \frac { \log 3 } { \log 7 } + \log 8 \right\}$ 
C)  $\left\{ \frac { \log 3 } { \log 7 } + 8 \right\}$ 
D)  $\left\{ \frac { \log 7 } { \log 3 } - 8 \right\}$ 
A)  $\{ \log 7 - \log 3 - \log 8 \}$ 
B)  $\left\{ \frac { \log 3 } { \log 7 } + \log 8 \right\}$ 
C)  $\left\{ \frac { \log 3 } { \log 7 } + 8 \right\}$ 
D)  $\left\{ \frac { \log 7 } { \log 3 } - 8 \right\}$

Question 11

Graph the exponential function.
-$f(x)=5^{x-1}$

Accepted Answer

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

Question 12

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

Accepted Answer

A)  $f ( x ) = 2 ^ { x } - 2$ 
B)  $f ( x ) = 2 ^ { x } + 2$ 
C)  $f ( x ) = 2 ^ { x - 2 }$ 
D)  $f ( x ) = 2 ^ { x }$ 
A)  $f ( x ) = 2 ^ { x } - 2$ 
B)  $f ( x ) = 2 ^ { x } + 2$ 
C)  $f ( x ) = 2 ^ { x - 2 }$ 
D)  $f ( x ) = 2 ^ { x }$

Question 13

Solve. Round the answer to the nearest whole.
-The number of students attending summer school at a local community college has been decreasing each year by $7 \%$. If 787 students currently attend summer school and this rate continues, find the number of students attending summer school in 5 years.

Accepted Answer

A)  519 students 
B)  578 students 
C)  548 students 
D)  550 students 
A)  519 students 
B)  578 students 
C)  548 students 
D)  550 students

Question 14

Solve the equation. Give an exact solution.
-$$8 ^ { 3 x } = 4.5$$

Accepted Answer

A)  $\left\{ \frac { 3 \log 4.5 } { \log 8 } \right\}$ 
B)  $\left\{ \frac { \log 4.5 } { 3 \log 8 } \right\}$ 
C)  $\left\{ \frac { \log 4.5 } { 8 \log 3 } \right\}$ 
D)  $\left\{ \frac { 4.5 \log 3 } { \log 8 } \right\}$ 
A)  $\left\{ \frac { 3 \log 4.5 } { \log 8 } \right\}$ 
B)  $\left\{ \frac { \log 4.5 } { 3 \log 8 } \right\}$ 
C)  $\left\{ \frac { \log 4.5 } { 8 \log 3 } \right\}$ 
D)  $\left\{ \frac { 4.5 \log 3 } { \log 8 } \right\}$

Question 15

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

Accepted Answer

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

Question 16

Determine whether the function is a one-to-one function.
-$\begin{array}{l|c|c|c|c|c|c}
\text { Month of } 1999 \text { (input) } & \text { Jan } & \text { Feb } & \text { Mar } & \text { Apr } & \text { May } & \text { Jun } \
\hline \begin{array}{l}
\text { Sales of Product B } \
\text { (output) }
\end{array} & 3410 & 3863 & 3108 & 3712 & 4014 & 3863
\end{array}$

Accepted Answer

A)  one-to-one 
B)  not one-to-one 
A)  one-to-one 
B)  not one-to-one

Question 17

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

Accepted Answer

A)  Yes 
B)  No 
A)  Yes 
B)  No

Question 18

Use the formula A $$A = P \left( 1 + \frac { r } { n } \right) ^ { n t } \text { or } A = P e ^ { r t } \text { to solve. }$$
-Suppose that you have $3000 to invest. Which investment yields the greater return over 7 years: 5.4% compounded monthly or 5.5% compounded quarterly?

Accepted Answer

A)  Both investment plans yield the same return. 
B)  $3000 invested at 5.5% compounded quarterly over 7 years yields the greater return. 
C)  $3000 invested at 5.4% compounded monthly over 7 years yields the greater return. 
A)  Both investment plans yield the same return. 
B)  $3000 invested at 5.5% compounded quarterly over 7 years yields the greater return. 
C)  $3000 invested at 5.4% compounded monthly over 7 years yields the greater return.

Question 19

Use the power property to rewrite the expression.
-$\log _ { \mathrm { r } } \mathrm { s }$

Accepted Answer

A)  $s \log _ { \mathrm { r } } \mathrm { t }$ 
B)  $t \log _ { \mathrm { r } } \mathrm { s }$ 
C)  $t \log _ { \mathrm { s } } \mathrm { r }$ 
D)  $r \log _ { \mathrm { s } } \mathrm { t }$ 
A)  $s \log _ { \mathrm { r } } \mathrm { t }$ 
B)  $t \log _ { \mathrm { r } } \mathrm { s }$ 
C)  $t \log _ { \mathrm { s } } \mathrm { r }$ 
D)  $r \log _ { \mathrm { s } } \mathrm { t }$

Question 20

Use the exponential decay formula to find the final amount. Round to the nearest whole.
-$\begin{array}{c|c|c|c}
\begin{array}{c}
\text { Original } \
\text { Amount }
\end{array} & \begin{array}{c}
\text { Decay } \
\text { Rate per Year }
\end{array} & \begin{array}{c}
\text { Number } \
\text { of Years, } \times
\end{array} & \begin{array}{c}
\text { Final Amount after } \
\text { x Years of Decay }
\end{array} \
\hline 207 & 4 \% & 7 &
\end{array}$

Accepted Answer

A)  291 
B)  155 
C)  272 
D)  156 
A)  291 
B)  155 
C)  272 
D)  156

Decide whether the statement is true or false. - $\log _ { 8 } 384 - \log _ { 8 } 48 = 1$

Solve the logarithmic equation. Give an exact solution. - $\log _ { 3 } ( x + 6 ) - \log _ { 3 } ( x - 3 ) = 3$

Use the exponential decay formula with half-lives to find the final amount. Round to the nearest tenth when necessary. - Original Amount Half-Life (in years) Number of Years Final Amount after x Time Intervals 26 125 800

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

Graph the function. - $f ( x ) = e ^ { 6 x }$ $Graph the function. - f ( x ) = e ^ { 6 x }$

Express as the logarithm of a single expression. Assume that variables represent positive numbers. - $\log _ { \mathrm { b } } \mathrm { u } + \log _ { \mathrm { b } } \mathrm { v }$

Write as an exponential equation. - $\log _ { 3 } \sqrt { 3 } = \frac { 1 } { 2 }$

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

Solve the equation. Give an exact solution. - $3 ^ { x + 8 } = 7$

Graph the exponential function. - $f(x)=5^{x-1}$ $Graph the exponential function. - f(x)=5^{x-1}$

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

Solve. Round the answer to the nearest whole. -The number of students attending summer school at a local community college has been decreasing each year by $7 \%$ . If 787 students currently attend summer school and this rate continues, find the number of students attending summer school in 5 years.

Solve the equation. Give an exact solution. - $8 ^ { 3 x } = 4.5$

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

Determine whether the function is a one-to-one function. - Month of 1999 (input) Jan Feb Mar Apr May Jun Sales of Product B (output) 3410 3863 3108 3712 4014 3863

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

Use the formula A $A = P \left( 1 + \frac { r } { n } \right) ^ { n t } \text { or } A = P e ^ { r t } \text { to solve. }$ -Suppose that you have $3000 to invest. Which investment yields the greater return over 7 years: 5.4% compounded monthly or 5.5% compounded quarterly?

Use the power property to rewrite the expression. - $\log _ { \mathrm { r } } \mathrm { s }$

Use the exponential decay formula to find the final amount. Round to the nearest whole. - Original Amount Decay Rate per Year Number of Years, \times Final Amount after x Years of Decay 207 4\% 7

Real Numbers and Algebraic Expressions

Equations, Inequalities, and Problem Solving

Graphs and Functions

Systems of Equations and Inequalities

Polynomials and Polynomial Functions

Rational Expressions

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Conic Sections

Fractions

Filters

Exam 9: Exponential and Logarithmic Functions

Decide whether the statement is true or false. - log⁡8384−log⁡848=1\log _ { 8 } 384 - \log _ { 8 } 48 = 1log8​384−log8​48=1

Solve the logarithmic equation. Give an exact solution. - log⁡3(x+6)−log⁡3(x−3)=3\log _ { 3 } ( x + 6 ) - \log _ { 3 } ( x - 3 ) = 3log3​(x+6)−log3​(x−3)=3

Use the exponential decay formula with half-lives to find the final amount. Round to the nearest tenth when necessary. - Original Amount Half-Life (in years) Number of Years Final Amount after x Time Intervals 26 125 800

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

Graph the function. - f(x)=e6xf ( x ) = e ^ { 6 x }f(x)=e6x

Express as the logarithm of a single expression. Assume that variables represent positive numbers. - log⁡bu+log⁡bv\log _ { \mathrm { b } } \mathrm { u } + \log _ { \mathrm { b } } \mathrm { v }logb​u+logb​v

Write as an exponential equation. - log⁡33=12\log _ { 3 } \sqrt { 3 } = \frac { 1 } { 2 }log3​3​=21​

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

Solve the equation. Give an exact solution. - 3x+8=73 ^ { x + 8 } = 73x+8=7

Graph the exponential function. - f(x)=5x−1f(x)=5^{x-1}f(x)=5x−1

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

Solve the equation. Give an exact solution. - 83x=4.58 ^ { 3 x } = 4.583x=4.5

Write as an exponential equation. - log⁡e1e3=−3\log _ { \mathrm { e } } \frac { 1 } { \mathrm { e } ^ { 3 } } = - 3loge​e31​=−3

Determine whether the function is a one-to-one function. - Month of 1999 (input) Jan Feb Mar Apr May Jun Sales of Product B (output) 3410 3863 3108 3712 4014 3863

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

Use the power property to rewrite the expression. - log⁡rs\log _ { \mathrm { r } } \mathrm { s }logr​s

Use the exponential decay formula to find the final amount. Round to the nearest whole. - Original Amount Decay Rate per Year Number of Years, \times Final Amount after x Years of Decay 207 4\% 7

Real Numbers and Algebraic Expressions

Equations, Inequalities, and Problem Solving

Graphs and Functions

Systems of Equations and Inequalities

Polynomials and Polynomial Functions

Rational Expressions

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Conic Sections

Fractions

Filters

Decide whether the statement is true or false. - $\log _ { 8 } 384 - \log _ { 8 } 48 = 1$

Solve the logarithmic equation. Give an exact solution. - $\log _ { 3 } ( x + 6 ) - \log _ { 3 } ( x - 3 ) = 3$

Graph the function. - $f ( x ) = e ^ { 6 x }$ $Graph the function. - f ( x ) = e ^ { 6 x }$

Express as the logarithm of a single expression. Assume that variables represent positive numbers. - $\log _ { \mathrm { b } } \mathrm { u } + \log _ { \mathrm { b } } \mathrm { v }$

Write as an exponential equation. - $\log _ { 3 } \sqrt { 3 } = \frac { 1 } { 2 }$

Solve the equation. Give an exact solution. - $3 ^ { x + 8 } = 7$

Graph the exponential function. - $f(x)=5^{x-1}$ $Graph the exponential function. - f(x)=5^{x-1}$

Solve the equation. Give an exact solution. - $8 ^ { 3 x } = 4.5$

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

Use the power property to rewrite the expression. - $\log _ { \mathrm { r } } \mathrm { s }$