Education Technology

# Activities

• ##### Subject Area

• Maths: Algebra I: Exponential Functions
• Maths: Calculus: Applications of the Derivative

9-12

60 Minutes

• ##### Device
• TI-89 / TI-89 Titanium

TI Connect™

• ##### Accessories

TI Connectivity Cable

## Logistic Growth, Differential Equations, Slope Fields

#### 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.

• 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