Question 1

Solve the equation for $s$.
-$\log (6 \mathrm{~s}-8)=\mathrm{r}-4$

Accepted Answer

A)  $\frac{12+r}{6}$ 
B)  $10^{12}+\mathrm{r}$ 
C)  $\frac{10^{\mathrm{r}-4}+8}{6}$ 
D)  $\frac{6}{12+\mathrm{r}}$ 
A)  $\frac{12+r}{6}$ 
B)  $10^{12}+\mathrm{r}$ 
C)  $\frac{10^{\mathrm{r}-4}+8}{6}$ 
D)  $\frac{6}{12+\mathrm{r}}$

Question 2

Write in logarithmic form.
-$4^{-3}=\frac{1}{64}$

Accepted Answer

A)  $-3=\log _{1 / 64} 4$ 
B)  $\frac{1}{64}=\log _{4}-3$ 
C)  $-3=\log _{4} \frac{1}{64}$ 
D)  $4=\log _{-3} \frac{1}{64}$ 
A)  $-3=\log _{1 / 64} 4$ 
B)  $\frac{1}{64}=\log _{4}-3$ 
C)  $-3=\log _{4} \frac{1}{64}$ 
D)  $4=\log _{-3} \frac{1}{64}$

Question 3

Graph the function.
-$f(x)=-\left(3^{x}\right)$

Accepted Answer

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

Question 4

Evaluate the expression.
-$\log _{7.4}300$

Accepted Answer

A)  0.3509 
B)  2.4771 
C)  2.8498 
D)  40.5405 
A)  0.3509 
B)  2.4771 
C)  2.8498 
D)  40.5405

Question 5

Solve the problem.
-In the formula $\mathrm{A}=\mathrm{Ie}^{\mathrm{kt}}, \mathrm{A}$ is the amount of radioactive material remaining from an initial amount I at a given time $t$ and $k$ is a negative constant determined by the nature of the material. An artifact is discovered at a certain site. If it has $79 \%$ of the carbon-14 it originally contained, what is the approximate age of the artifact? (carbon-14 decays at the rate of $0.0125 \%$ annually.) (Round to the nearest year.)

Accepted Answer

A) 6 $320 \mathrm{yr}$ 
B)  $1886 \mathrm{yr}$ 
C)  1680 yr 
D)  819 yr 
A) 6 $320 \mathrm{yr}$ 
B)  $1886 \mathrm{yr}$ 
C)  1680 yr 
D)  819 yr

Question 6

Solve the problem.
-The decay of $163 \mathrm{mg}$ of an isotope is given by $\mathrm{A}(\mathrm{t})=163 \mathrm{e}^{-0.014 \mathrm{t}}$, where $\mathrm{t}$ is time in years. Find the amount left after 13 years.

Accepted Answer

A)  136 
B)  161 
C)  134 
D)  68 
A)  136 
B)  161 
C)  134 
D)  68

Question 7

Match the equation to the graph.
-

Accepted Answer

A)  $y=10^{x}$ 
B)  $y=e^{x}$ 
C)  $y=\log x$ 
D)  $y=\ln x$ 
A)  $y=10^{x}$ 
B)  $y=e^{x}$ 
C)  $y=\log x$ 
D)  $y=\ln x$

Question 8

Solve the equation.
-$\log (x+9)=1-\log x$

Accepted Answer

A)  1 
B)  1,10 
C)  -1 
D)  $-10,1$ 
A)  1 
B)  1,10 
C)  -1 
D)  $-10,1$

Question 9

Write the logarithmic and exponential equations associated with the display.
-$f(x)=\log x$

Accepted Answer

A)  $\log 2=0.30102999566 ; 10^{0.30102999566}=2$ 
B)  $\log 2=0.69314718056 ; 10^{0.69314718056}=2$ 
C)  $\log 0.30102999566=2 ; 10^{2}=0.30102999566$ 
D)  $\log 0.69314718056=2 ; 10^{2}=0.69314718056$ 
A)  $\log 2=0.30102999566 ; 10^{0.30102999566}=2$ 
B)  $\log 2=0.69314718056 ; 10^{0.69314718056}=2$ 
C)  $\log 0.30102999566=2 ; 10^{2}=0.30102999566$ 
D)  $\log 0.69314718056=2 ; 10^{2}=0.69314718056$

Question 10

Write the word or phrase that best completes each statement or answers the question.
-$f(x)=a^{x}$
   The graph of an exponential function with base a is given. Sketch the graph of $g(x)=a^{x+2}$. Give the domain and range of $g$.

Accepted Answer

@#IMG-DLM& 
domain:

Question 11

Solve the problem.
-How long must $\$ 4700$ be in a bank at $6 \%$ compounded annually to become $\$ 7067.06$ ? (Use the function $\mathrm{P}(\mathrm{t})=\mathrm{P}_{0} \mathrm{e}^{\mathrm{kt}}$, where $\mathrm{P}_{0}$ is the amount initially placed in savings, $\mathrm{t}$ is the time in years, and $\mathrm{P}(\mathrm{t})$ is the balance after time $\mathrm{t}$. Round to the nearest year.)

Accepted Answer

A)  8 yr 
B)  $9 \mathrm{yr}$ 
C)  $6 \mathrm{yr}$ 
D)  $7 \mathrm{yr}$ 
A)  8 yr 
B)  $9 \mathrm{yr}$ 
C)  $6 \mathrm{yr}$ 
D)  $7 \mathrm{yr}$

Question 12

Solve the equation for $s$.
-$3-\mathrm{r}=\log (6 \mathrm{~s}+6)$

Accepted Answer

A)  $\frac{9+r}{6}$ 
B)  $\frac{6}{9+r}$ 
C)  $10^{9}+\mathrm{r}$ 
D)  $\frac{10^{3-r}-6}{6}$ 
A)  $\frac{9+r}{6}$ 
B)  $\frac{6}{9+r}$ 
C)  $10^{9}+\mathrm{r}$ 
D)  $\frac{10^{3-r}-6}{6}$

Solve the equation for $s$ . - $\log (6 \mathrm{~s}-8)=\mathrm{r}-4$

Write in logarithmic form. - $4^{-3}=\frac{1}{64}$

Graph the function. - $f(x)=-\left(3^{x}\right)$ $Graph the function. - f(x)=-\left(3^{x}\right)$

Evaluate the expression. - $\log _{7.4}300$

Solve the problem. -The decay of $163 \mathrm{mg}$ of an isotope is given by $\mathrm{A}(\mathrm{t})=163 \mathrm{e}^{-0.014 \mathrm{t}}$ , where $\mathrm{t}$ is time in years. Find the amount left after 13 years.

Match the equation to the graph. -

Solve the equation. - $\log (x+9)=1-\log x$

Write the logarithmic and exponential equations associated with the display. - $f(x)=\log x$ $Write the logarithmic and exponential equations associated with the display. - f(x)=\log x$

Solve the equation for $s$ . - $3-\mathrm{r}=\log (6 \mathrm{~s}+6)$

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Exam 4: Exponential and Logarithmic Functions

Solve the equation for sss . - log⁡(6 s−8)=r−4\log (6 \mathrm{~s}-8)=\mathrm{r}-4log(6 s−8)=r−4

Write in logarithmic form. - 4−3=1644^{-3}=\frac{1}{64}4−3=641​

Graph the function. - f(x)=−(3x)f(x)=-\left(3^{x}\right)f(x)=−(3x)

Evaluate the expression. - log⁡7.4300\log _{7.4}300log7.4​300

Solve the problem. -The decay of 163mg163 \mathrm{mg}163mg of an isotope is given by A(t)=163e−0.014t\mathrm{A}(\mathrm{t})=163 \mathrm{e}^{-0.014 \mathrm{t}}A(t)=163e−0.014t , where t\mathrm{t}t is time in years. Find the amount left after 13 years.