Question 1

The total number $N$ of bacteria cells in a petri dish when exposed to a new drug can be approximated by the function $\mathrm{N}(\mathrm{x})=75 \mathrm{e}^{-0.02532 \mathrm{x}}$, where $\mathrm{N}$ is measured in thousands; and $\mathrm{x}=0$ corresponds to the initial number of cells, $\mathrm{x}=1$ corresponds to the number of cells after one hour, and so on. The function is graphed on a graphing calculator-generated screen. Interpret the meanings of $x$ and $y$ in the display at the bottom of the screen.

Accepted Answer

A)  It means that the drug is helping the bacteria grow. 
B)  It means that after 75 hours, there will be approximately 45,200 bacteria cells. 
C)  It means that after 20 hours, there will be approximately 45,200 bacteria cells. 
D)  It means that after 20 hours, there will be approximately 45 bacteria cells.

Question 2

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one."
-$f(x)=\frac{8}{x-9}$

Accepted Answer

A)  $f^{-1}(x)=\frac{-9+8 x}{x}$ 
B)  Not one-to-one 
C)  $f^{-1}(x)=\frac{9 x+8}{x}$ 
D)  $f^{-1}(x)=\frac{x}{-9+8 x}$

Question 3

Solve the equation.
-$\log _{x} 625=4$

Accepted Answer

A)  5 or -5 
B)  4 or -4 
C)  4 
D)  5

Question 4

A student argues that the best choice for the logarithmic base to be used in solving $7 \mathrm{X}=50$ is 7 . What is wrong with this thinking?

Accepted Answer

The answer of A student argues that the best choice...

Question 5

Jorge invested $\$ 7500$ at $8 \%$ compounded semiannually. In how many years will Jorge's investment have tripled? Round your answer to the nearest tenth of a year.

Accepted Answer

A)  13.7 years 
B)  1.5 years 
C)  14 years 
D)  6.2 years

Question 6

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one."
-$f(x)=4 x-6$

Accepted Answer

A)  $f^{-1}(x)=\frac{x-6}{4}$ 
B)  $f^{-1}(x)=\frac{x}{4}+6$ 
C)  Not one-to-one 
D)  $f^{-1}(x)=\frac{x+6}{4}$

Question 7

Solve the equation.
-$4^{(1+2 \mathrm{x})}=1024$

Accepted Answer

A)  $\{8\}$ 
B)  $\{-2\}$ 
C)  $\{2\}$ 
D)  $\{256\}$

Question 8

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one."
-$f(x)=x^{3}-5$

Accepted Answer

A)  Not one-to-one 
B)  $f^{-1}(x)=x+5$ 
C)  $f^{-1}(x)= \pm \sqrt[3]{x+5}$ 
D)  $f^{-1}(x)=\sqrt[3]{x+5}$

Question 9

Barry Newman's savings account has a balance of $\$ 1964$. After 10 years, what will the amount of interest be at $8 \%$ compounded annually?

Accepted Answer

A)  $\$ 2276.13$ 
B)  $\$ 2267.13$ 
C)  $\$ 1571.20$ 
D)  $\$ 2281.13$

Question 10

Write in exponential form.
-$\log _{-2}-8=\mathrm{x}$

Accepted Answer

A)  $\{16\}$ 
B)  $\{-10\}$ 
C)  $\{4\}$ 
D)  $\{3\}$

Question 11

A certain noise has an intensity $I$ of $1.91 \times 10^{-5}$. Given that decibel level $D$ is related to intensity by $\mathrm{D}=10 \log \left(\frac{\mathrm{I}}{\mathrm{I}_{\mathrm{O}}}\right)$, where $\mathrm{I}_{\mathrm{O}}$ is $10^{-12}$, determine the decibel level of the noise. Round your answer to the nearest decibel.

Accepted Answer

A)  7 decibels 
B)  63 decibels 
C)  168 decibels 
D)  73 decibels

Question 12

The population of a particular city is increasing at a rate proportional to its size. It follows the function $\mathrm{P}(\mathrm{t})=1+\mathrm{ke} 0.08 \mathrm{t}$ where $\mathrm{k}$ is a constant and $\mathrm{t}$ is the time in years. If the current population is 12,000 , in how many years is the population expected to be 30,000 ? (Round to the nearest year.)

Accepted Answer

A)  $11 \mathrm{yr}$ 
B)  $69 \mathrm{yr}$ 
C)  $6 \mathrm{yr}$ 
D)  $5 \mathrm{yr}$

Exam 10: Inverse, Exponential, and Logarithmic Functions

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one." - $f(x) =\frac{8}{x-9}$

Solve the equation. - $\log _{x} 625=4$

A student argues that the best choice for the logarithmic base to be used in solving $7 \mathrm{X}=50$ is 7 . What is wrong with this thinking?

Jorge invested $\$ 7500$ at $8 \%$ compounded semiannually. In how many years will Jorge's investment have tripled? Round your answer to the nearest tenth of a year.

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one." - $f(x) =4 x-6$

Solve the equation. - $4^{(1+2 \mathrm{x}) }=1024$

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one." - $f(x) =x^{3}-5$

Barry Newman's savings account has a balance of $\$ 1964$ . After 10 years, what will the amount of interest be at $8 \%$ compounded annually?

Write in exponential form. - $\log _{-2}-8=\mathrm{x}$

Exam 10: Inverse, Exponential, and Logarithmic Functions

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one." - f(x) =8x−9f(x) =\frac{8}{x-9}f(x) =x−98​

Solve the equation. - log⁡x625=4\log _{x} 625=4logx​625=4

A student argues that the best choice for the logarithmic base to be used in solving 7X=507 \mathrm{X}=507X=50 is 7 . What is wrong with this thinking?

Jorge invested $7500\$ 7500$7500 at 8%8 \%8% compounded semiannually. In how many years will Jorge's investment have tripled? Round your answer to the nearest tenth of a year.

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one." - f(x) =4x−6f(x) =4 x-6f(x) =4x−6

Solve the equation. - 4(1+2x) =10244^{(1+2 \mathrm{x}) }=10244(1+2x) =1024

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one." - f(x) =x3−5f(x) =x^{3}-5f(x) =x3−5

Barry Newman's savings account has a balance of $1964\$ 1964$1964 . After 10 years, what will the amount of interest be at 8%8 \%8% compounded annually?

Write in exponential form. - log⁡−2−8=x\log _{-2}-8=\mathrm{x}log−2​−8=x

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one." - $f(x) =\frac{8}{x-9}$

Solve the equation. - $\log _{x} 625=4$

A student argues that the best choice for the logarithmic base to be used in solving $7 \mathrm{X}=50$ is 7 . What is wrong with this thinking?

Jorge invested $\$ 7500$ at $8 \%$ compounded semiannually. In how many years will Jorge's investment have tripled? Round your answer to the nearest tenth of a year.

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one." - $f(x) =4 x-6$

Solve the equation. - $4^{(1+2 \mathrm{x}) }=1024$

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one." - $f(x) =x^{3}-5$

Barry Newman's savings account has a balance of $\$ 1964$ . After 10 years, what will the amount of interest be at $8 \%$ compounded annually?

Write in exponential form. - $\log _{-2}-8=\mathrm{x}$