Modeling Real World Events By: 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!

 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

 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 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.

Run Number Time of Run in Seconds seconds seconds seconds seconds

 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.

 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

 Roberts, Donna. "Exponential Growth and Decay." Exponential Growth and Decay. Oswego City School District Regents Exam Prep Center, n.d. Web. 07 Apr