Creating Exponential Equations

Modeling Real World EventsBy: Mr. Sheldon

DLT: I will create exponential equations from real-world situations and use those equations to predict future outcomes.

You have already collected the data for today’s activity. Now let’s see how it relates to Algebra!

What are we doing today?

An exponential equation is the function with the general form with three rules.◦ a is not equal to zero◦ b>0 and is not equal to one◦ x is a real number

Exponential Equations

All exponential equations will either grow or decay.

Exponential growth will occur when b>1◦ The graph will grow as x grows

Exponential decay will occur when 0<b<1◦ The graph will approach an asymptote as x grows

Exponential Growth/Decay

Pictures from regentsprep.org

Before this lesson, I went for a run. Well actually I ran some sprints. Anyway, with each sprint I ran my time grew. I noticed that, when graphed, the times were non-linear. They were not even quadratic. They formed an exponential growth graph.

Let’s look at my times and see how I created my exponential equation for running sprints.

Now to the experiments

Run Number Time of Run in Seconds

1 9.45 seconds

2 9.90 seconds

3 12.00 seconds

4 17.37 seconds

5 22.32

My Times

To create the equation I will use the general equation of .

1. First, I will insert my initial point and solve for a. 2. Next, I will sub that in for a and solve for b.3. Then, I will use b to find my numerical value for

a.4. Finally, put everything into the general form and

you have your equation. Let’s see how it works.

Creating the Equation

(1, 9.45) and (5, 22.32)

My Work

Work with your group to create an exponential equation using your first data entry and your last data entry.

Once your group has created the equation, get my attention.

If your work is correct, then I will assign you your homework from the data.

Do you want me to put the last page up?◦ *Hint: There is an example in the textbook on page 432

Your turn!

Roberts, Donna. "Exponential Growth and Decay." Exponential Growth and Decay. Oswego City School District Regents Exam

Prep Center, n.d. Web. 07 Apr. 2013.

Pictures Citation