Unit 5 Review Questions

Emily would like to buy some new furniture for her home. She decides to buy the furniture on credit with 9.5% interest compounded quarterly. If she spent $7,400, how much total will she have paid after 8 years.

What is the solution to the equation:
 $4e^{3t}=80$ 

•  $t=\frac{\ln\left(80\right)}{3\ln\left(4\right)}$  
  

•  $t=\frac{\ln\left(20\right)}{3}$  
  

•  $t=\frac{\ln\left(80\right)}{12}$ 

•  $t=\ln\left(\frac{20}{3}\right)$  

A population of fish starts at 8,000 and decreases by 6% per year. What is the population of fish after 10 years? Round to the nearest whole number.

Numeric value only.

The number of mosquitoes at the beginning of the summer was 4,000. The population of mosquitoes is expected to grow at a rate of 25% a month. How many mosquitoes will there be after 4 months? Round to the nearest whole number.

Numeric value only.

What is the range of this function?

• (-∞,0)

• [4,∞)

• (-∞,4)

• (4,∞)

Solve. 
4^(6x-12)=7

• 1.40

• 2.23

• 13.40

• 3

Find the time required for an investment of $1000 to grow to $5000 at an interest rate of 8% per year compounded monthly. (round to nearest year)

• 1 year

• 242 years

• 20 years

• 13 years

Solve:

 $-6\log_3\left(x-3\right)=-24$  

• 5

• 13

• 84

• -20

Find $f^{-1}\left(x\right)$  given  $f\left(x\right)=8^x$   

•  $f^{-1}\left(x\right)=\frac{1}{8^x}$  

•  $f^{-1}\left(x\right)=\log\left(x\right)$  

•  $f^{-1}\left(x\right)=\log_x\left(8\right)$  

•  $f^{-1}\left(x\right)=\log_8\left(x\right)$  

What is the asymptote of the equation: $f\left(x\right)=\log_4\left(x-5\right)$ 

• x = 5

• x = 0

• y = 5

• x = 4

• DNE