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?

• $$y=2\left(\frac{4}{3}\right)^x$$  

• $$y=\frac{1}{4}\left(2\right)^x$$  

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

• $$y=2\left(\frac{2}{5}\right)^x$$  

Fill in the Blanks

Find the amount in a continuously compounded account for the given conditions.

Principal: $5,000

annual interest rate: 6.9%

time: 30 years

Fill in the Blanks

Suppose you deposit $6,000 in a savings account that pays interest at an annual rate of 4%, compounded continuously. How many years will it take for the balance in your savings account to reach $8000.

Round your answer up to the nearest number of years.

(Convert to logarithmic form to solve)

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.

$$2^9=512$$  

• $$\log_9512=2$$  

• $$\log_92=512$$  

• $$\log_2512=9$$  

• $$\log_29=512$$  

Fill in the Blanks

Evaluate the logarithm without using a calculator.

$\log_77^6$  

Fill in the Blanks

Evaluate the logarithm without using a calculator.

$\log_{\frac{1}{3}}\left(\frac{1}{9}\right)$  

Fill in the Blanks

Evaluate the logarithm without using a calculator.

$\log_927$  

Fill in the Blanks

Solve the equation for x.

$2+\log_5x=3$  

Fill in the Blanks

Solve the equation for x. Round to the nearest thousandth.

$4^{\left(x+2\right)}-16=60$  

Fill in the Blanks

Solve the equation for x. Round to the nearest whole number.

$2\ln\left(x-5\right)=25$  

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

• $$\log_28$$  

• $$\log_2\left(4\right)$$  

• $$\log_82$$