<meta http-equiv="refresh" content="1; url=/nojavascript/"> Modeling Data | CK-12 Foundation
Dismiss
Skip Navigation

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 TI-83, 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 to L6 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 L1-L6.

Associated Materials

Problem 1 – Exponential Growth

In this problem, students will graph data given in L1 and L2.

Students should determine an equation for the data using their knowledge of compound interest equations.

The equation is y = 1000(1.04)^x.

Students can plot the function to determine if it goes through the graphed points by pressing Y= and entering the function.

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 L1 and L2. Students should determine an equation for the data using the regression capabilities of the graphing calculator.

Note: to find Y1, press VARS, scroll over to Y-VARS, select 1:Function..., and select 1:Y1.

The equation is y = 8.6 \times 10^{-8} + 0.369 \times \ln x.

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 y = 1250(0.85)^x.

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?

Image Attributions

Description

Authors:

Grades:

Date Created:

Feb 23, 2012

Last Modified:

Apr 29, 2014
You can only attach files to None which belong to you
If you would like to associate files with this None, please make a copy first.

Reviews

Please wait...
Please wait...
Image Detail
Sizes: Medium | Original
 
TI.MAT.ENG.TE.1.Calculus.2.1

Original text