Exponentials and Logarithms Practice

Exponentials and Logarithms Practice

By CHRISTINA SHUTE

​Exponential Growth/Decay

Multiple Choice

Determine whether the function represents exponential growth or decay.

$$y=20\left(1.75\right)^x$$  

• Growth

• Decay

Multiple Choice

Determine whether the function represents exponential growth or decay.

$$y=0.25\left(1.05\right)^x$$  

• Growth

• Decay

Multiple Choice

Write an exponential function to model the situation.

A population of 123,600 grows 1.3% per year.

• $$f\left(x\right)=123600\left(1.013\right)^x$$  

• $$f\left(x\right)=123600\left(0.987\right)^x$$  

• $$f\left(x\right)=1236\left(1.013\right)^x$$  

• $$f\left(x\right)=1236\left(0.987\right)^x$$  

Multiple Choice

A population of 123,600 grows 1.3% per year.

Find the population after 10 years.

•  1

• 419,569 

• 108,440 

• 140,641 

Open Ended

A new car that sells for $18,000 depreciates 25% each year for 4 years. Calculate the value of the car after 4 years.

Multiple Choice

Which of the following functions represents exponential decay and has a y-intercept of 2?

• $$y=2\left(\frac{4}{3}\right)^x$$  

• $$y=\frac{1}{4}\left(2\right)^x$$  

• $$y=\frac{1}{2}\left(0.95\right)^x$$  

• $$y=2\left(\frac{2}{5}\right)^x$$  

Since exponential and logarithmic functions are inverses, you can use this pattern to convert between them.

Multiple Choice

Write the equation in logarithmic form.

$$9^2=81$$  

• $$\log_92=81$$  

• $$\log_981=2$$  

• $$\log_281=9$$  

• $$\log_29=81$$  

Multiple Choice

Write the equation in logarithmic form.

$$2^9=512$$  

• $$\log_9512=2$$  

• $$\log_92=512$$  

• $$\log_2512=9$$  

• $$\log_29=512$$  

Open Ended

A single-celled bacterium divides every hour. The number N of bacteria after t hours is given by the formula $$\log_2N=t$$  . After how many hours will there be 32 bacteria?

Multiple Choice

How does the graph of $$y=\log_5\left(x-3\right)$$  compare with the graph of the parent function, $$y=\log_5x$$  ?

• translated 3 units to the left

• translated 3 units down

• translated 3 units to the right

• translated 3 units up

Open Ended

Describe how the graph of the function $$y=\log_2\left(x+1\right)-5$$   compares with the graph of the parent function $$y=\log_2x$$  .

Multiple Choice

Find the inverse of the function.

$$y=\log_2x$$  

• $$x=2^y$$  

• $$y=-\log_2x$$  

• $$y=2^x$$  

• $$x=\log_2y$$  

Multiple Choice

Find the inverse of the function.

$$y=\log\left(x+4\right)$$  

• $$y=10^x$$  

• $$y=10^{x-4}$$  

• $$y=10^x+4$$  

• $$y=10^x-4$$  

Multiple Choice

Write the expression as a single logarithm.

$$\log_54+\log_53$$  

• $$\log_{12}5$$  

•   $$\log_512$$  

• $$\log_5\left(\frac{4}{3}\right)$$   

• $$\log_5\left(1\right)$$   

Multiple Choice

Write the expression as a single logarithm.

$$\log_24+\log_22-\log_28$$  

• 0

• $$\log_28$$  

• $$\log_2\left(4\right)$$  

• $$\log_82$$