Review of Exponential Functions

Teacher: Mr. Steven A. Manges

Why am I doing this?This interactive review will be completed as a review of

exponential functions. You are to read each of the screens before moving on. All moves from screen to screen will be done by using the buttons that I have provided for you. This review is to be completed from start to finish. Each section will contain information that is important to your understanding of exponential functions. After you have finished reviewing the information you will need to answer question(s) about that information. If you answer it correctly, you will be directed to the next section. If you miss the question, you will be sent back to the information to go over it again. This will continue until you answer the question correctly.

This is to be a learning experience but also fun. So let’s get ready to journey deep into the fun loving world of exponential functions.

Objectives for the review

• Correctly identify equations and graphs of exponential growth and decay

• Determine if exponential functions are correctly applied to a particular situation

• Correctly calculate the growth and decay rate, and the percent of growth or decay.

• Correctly calculate an exponential regression equation for a set of data.

What is exponential growth?

Remember that an exponential function is in the form,

y = a*bx, where a > 1, b > 0, b 1.

NOW! An exponential function that depicts growth is in the same form, but there is a restriction on the b value.

b > 1

Here is your first quiz.

Which of the following exponential equation is depicting exponential growth?

f(x) = 1.3*.4x

f(x) = 2*1.5x

f(x) = 7*

f(x) = 2*.9x

x

43

A

B

C

D

Way to go, kid!

What is exponential decay?

As we said before an exponential function is in the form,

y = a*bx, where a > 1, b > 0, b 1.

An exponential function depicting decay has the following restriction.

0 < b > 1

Here is your quiz on exponential decay:

Which of the following exponential equations is depicting exponential decay?

f(x) = 2*1.5x

f(x) = .2*3x

f(x) = 1.7*.1x

f(x) = 6*2.3x

A

B

C

D

Way to go, kid!

Graphs of Exponential Functions!

Below you will find graphs of two exponential functions. Examine these graph, then when you are ready click the next button to take the quiz.

Which graph is depicting Exponential Growth? But remember

if you must chose, chose wisely!

Remember, in exponential growth as x increase so does y!

Let’s remember that there are many applications for exponential functions. For example, if you have a savings account the interest compounded is done exponential. As you saw with the workbook activity, the world population is exponentially growing. Other examples would be insurance rates, a person income from year to year, bacteria decay, etc.

All of these are examples of why it is important for people to learn about exponential functions.

Applications of Exponential Functions

Which of the following is not an example of an application of exponential functions?

A banker is attempting to calculate the amount of money in a customer’s savings account.

The Census bureau is attempting to find out when the world population will reach 7 billion.

Mr. Manges is attempting to find out how long it will take for him to drive to Maine if his average speed is 60 mph.

A scientist is measuring the amount of bacteria on a toilet seat.

A

B

C

D

Way to go, kid!

Finding the growth/decay rate and percent of growth/decay

Below you will find the general form of an exponential function. Let’s focus on the b value.

y = a*bx

To determine the growth/decay rate simply look at the b value, copy it down and you have the rate.

To find the percent of growth use the formula below:

100(b - 1) = percent of growth

To find the percent of decay use the formula below:

100(1 - b) = percent of decay

What is the growth/decay rate and percent of growth/decay for the following equation?

y = 1.2*.5x

Growth rate of 1.2; 120%

increase

Decay rate of .5; 50% decrease

Growth rate of .5; 150% increase

Decay rate of 1.2; 12% decrease

A

B

C

D

Finding the growth/decay rate and percent of growth/decay

Below you will find the general form of an exponential function. Let’s focus on the b value.

y = a*bx

To determine the growth/decay rate simply look at the b value, copy it down and you have the rate.

To find the percent of growth use the formula below:

100(b - 1) = percent of growth

To find the percent of decay use the formula below:

100(1 - b) = percent of decay

What is the growth/decay rate and percent of growth/decay for the following equation?

y = 2*3.5x

Growth rate of 2; 200% increase

Decay rate of 3.5; 350% decrease

Growth rate of 3.5; 250%

increase

Decay rate of 2; 20% decrease

A

B

C

D

Find the regression equation for a set of data, depicting exponential growth/decay.

Select two adjacent y-values from your data. Take the higher x-valued number and divided it by the smaller x-valued number. This is your growth or decay rate.

Select a point from your data and substitute it into the equation y = a*bx, along with multiplier you calculate.

Click the next button to see an example.

Example of finding a regression equation.

x y

0 1.6

1 0.32

2 0.064

3 0.0128

4 0.00256

5 0.00051

The two y-values that will be selected are 0.064 and 0.0128. The corresponding x values are 0 and 1, respectively. Therefore 0.0128 will be divided by 0.064, hence 0.0128/0.064. This quotient equals 0.2. This is the b value.

To find the a value the point (0, 1.6) will be used. Substitute the point into the exponential function and solve.

1.6 = a*(.20)

a = 1.6

The regression equation is y = 1.6*.2x

What is the regression equation for the data in the table?

x y

0 .5

1 .6

2 .72

3 .864

4 1.0368

5 1.2442

y = 1.2*.5x

y = .5*1.2x

y = 1.5*.2x

y = 2.5*2.2x

A

B

C

D

You have finished the exponential functions review show!

END!