2.1: Modeling Data
This activity is intended to supplement Calculus, Chapter 1, Lesson 3.
ID: 12316
Time required: 20 minutes
Activity Overview
In this activity, students will graph data modeling exponential and logarithmic growth and find equations representing the data.
Topic: Modeling Growth
 Exponential Growth and Decay
 Compound Interest
 Logarithmic Growth
Teacher Preparation and Notes
 This activity can be used with the TI83, 84, or 89. This supplement is geared towards the 83 and 84.
 Students should be aware of the compound interest formula in order to be able to find the growth of the exponential data given in Problem 1.
 Students should be aware of basic logarithms in order to determine the base of the log function for Problem 2.

The lists
L1 toL6 will need to be loaded into the student calculators before beginning this activity.  To download the list files, go to http://www.education.ti.com/calculators/downloads/US/Activities/Detail?id=12316 and select L1L6.
Associated Materials
 Student Worksheet: Modeling Data http://www.ck12.org/flexr/chapter/9726
 L1.8xl, L2.8xl, L3.8xl, L4.8xl, L5.8xl, and L6.8xl
Problem 1 – Exponential Growth
In this problem, students will graph data given in
Students should determine an equation for the data using their knowledge of compound interest equations.
The equation is
Students can plot the function to determine if it goes through the graphed points by pressing
Discussion Questions
 What variable should be on the horizontal axis? Vertical axis?
 How can you determine the interest rate for this growth?
Problem 2 – Logarithmic Growth
In this problem, students will graph data given on
Note: to find
The equation is
Discussion Questions
 What variable should be on the horizontal axis? Vertical axis?
Extension Problem – Exponential Decay
In this problem, students will continue with the process in the first two problems. The given data represents exponential decay.
The equation is
Discussion Questions
 What is the number of acres the farmer started with in year zero?
 By what percent does the amount of acres available decrease every year?