ExponentialFunctionWordProblems

Exponential Functions

The variable “a” represents the initial amount.

The variable “r” represents the growth rate.

The variable “t” represents the amount of time.

Multiple Choice

In the given equation, $$y=\frac{3}{5}\left(\frac{8}{7}\right)^x$$ , what is the value of a?

• $$a=\frac{3}{5}$$

• $$a=\frac{8}{7}$$

• $$a=1$$

• $$a=0$$

Fill in the Blanks

In the given equation, $f\left(x\right)=\frac{3}{5}\left(\frac{8}{7}\right)^x$ , type in if the equation will produce a graph of exponential growth or exponential decay (type in for example: exponential decay if the graph is decaying).

Multiple Choice

The original value of an investment is $1400, and the value increases by 9% each year. Use an exponential growth function to find the value of the investment after 25 years. Which equation would represent the exponential function?

• $$y=1+0.09\left(1400\right)^{25}$$

• $$y=1400\left(1+0.09\right)^{25}$$

• $$y=25\left(1+0.09\right)^{1400}$$

• $$y=1+0.09\left(25\right)^{1400}$$

Multiple Choice

The original value of an investment is $1400, and the value increases by 9% each year. Use an exponential growth function to find the value of the investment after 25 years. How much money would be invested after 25 years?

• $12,072.31

• $11,075.52

• $10,161.02

• $9,322.04

Draw

The cost of tuition at a college is $12,000 and is increasing at a rate of 6% each year. Use an exponential function to find the tuition cost after 4 years. Write an exponential function to represent the given situation ( $$y=a\cdot b^x$$ ). Write your response on the chalkboard.

Multiple Choice

The cost of tuition at a college is $12,000 and is increasing at a rate of 6% each year. Use an exponential function to find the tuition cost after 4 years. What is the tuition cost after 4 years?

• $12,720

• $13,483.20

• $14,292.19

• $15,149.72

Fill in the Blanks

The number of student athletes at a local high school is 300 and is increasing at a rate of 8% per year. Use an exponential function to find the number of student athletes after five years. Write the equation in the form ( $y=a\cdot b^x$ ).

Multiple Choice

The number of student athletes at a local high school is 300 and is increasing at a rate of 8% per year. Use an exponential function to find the number of student athletes after five years. What is the number of student athletes after 5 years? (Round your answer to the nearest whole student)

• 350

• 378

• 408

• 441

Draw

Circle the number that best represents where you are in learning the material.

The variable “a” represents the initial amount.

The variable “r” represents the decay rate.

The variable “t” represents the amount of time.

Multiple Choice

In the given equation, $$y=\left(\frac{5}{11}\right)^x$$ , what is the value of a?

• $$a=\frac{5}{11}$$

• $$a=x$$

• $$a=1$$

• $$a=0$$

Fill in the Blanks

In the given equation, $f\left(x\right)=\frac{9}{5}\left(\frac{3}{4}\right)^x$ , type in if the equation will produce a graph of exponential growth or exponential decay (type in for example: exponential growth if the graph is growing).

Multiple Choice

The population of a town is decreasing at a rate of 1% per year. In 2000, there were 1,300 people. Use an exponential function to find the population. Which equation would represent the exponential function?

• $$y=1-0.01\left(1300\right)^8$$

• $$y=8\left(1-0.01\right)^{1300}$$

• $$y=1300\left(1-0.01\right)^8$$

• $$y=8\left(1300\right)^{1-.01}$$

Multiple Choice

The population of a town is decreasing at a rate of 1% per year. In 2000, there were 1,300 people. Use an exponential function to find the population in 2008. Round your answer to the nearest whole value.

• 1,236

• 1,224

• 1,212

• 1,200

Draw

The value of a car is $18,000 and depreciating at a rate of 12% per year. Use an exponential function to find the value of the car after 10 years. Write an exponential function to represent the given situation ( $$y=a\cdot b^x$$ ). Write your response on the chalkboard.

Multiple Choice

The value of a car is $18,000 and depreciating at a rate of 12% per year. Use an exponential function to find the value of the car after 10 years.

• $5,013.02

• $5,696.61

• $6,473.42

• $7,356.16

Draw

A farmer buys a tractor for $50,000. If the tractor depreciates 10% per year, use an exponential function to find the value of the tractor in 7 years. Write the equation in the form ( $$y=a\cdot b^x$$ ). Write your equation down in the chalkboard background.

Multiple Choice

A farmer buys a tractor for $50,000. If the tractor depreciates 10% per year, use an exponential function to find the value of the tractor in 7 years. (Round your answer to the nearest whole dollar.)

• $29,525

• $26,572

• $23,915

• $21,523

Draw

Circle the number that best represents where you are in learning the material.