Education Technology

Logistic Growth, Differential Equations, Slope Fields

Published on 08/02/2005

Activity Overview

In this Computer Algebra System (CAS) activity, students investigate differential equations analytically, graphically and numerically and see relationships between the three approaches.

Before the Activity

  • Install TI Connect™ using the TI connectivity cable
  • See the attached PDF file for detailed instructions for this activity
  • Print pages 1 - 2 from the attached PDF file for the class
  • During the Activity

    Distribute the pages to the class.

    Follow the Activity procedures:

  • Use the random number generator to generate logistic data to simulate the spread of disease
  • Use the data analyzing features of the calculator to create a scatter plot
  • Find a logistic regression curve to fit the data
  • Use analytic methods to find the solution to the differential equation for logistic growth
  • Graph the solution along with the original scatter plot
  • Use the differential equation graphing mode to see numerical and visual solutions without finding the analytical solution
  • Note that the visual solution includes a slope field and the numerical solution includes tables
  • After the Activity

    Students' answer questions on the Activity sheet.

    Review student results:

  • As a class, discuss questions that appeared to be more challenging
  • Re-teach concepts as necessary