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Activity Overview

In this activity, students use the calculator to find numerical solution for a function given its derivative and a point on the function.

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Before the Activity

See the attached PDF file for detailed instructions for this activity
Print pages 17 - 25 from the attached PDF file for your class
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During the Activity

Distribute the pages to the class.

Follow the Activity procedures:

A Table of Values for a Differential Equation:

Enter the differential equation on the calculator
Select initial conditions, window viewing parameters, and graphing parameters
Graph the solution to the differential equation
Use the trace function and trace values of y for different values of x
Generate a table of values with all the ordered pairs
Compare results in the table (numerical solution) to the values given by the analytic solution
Exponential Growth:

Enter the differential equation
Select initial conditions, window viewing parameters, and graphing parameters
Graph the solution to the differential equation
Enter the analytic solution and compare it to the graphed solution
Generate a table of values for the equation and compare the values to the analytic solution
Compound Interest:

Formulate a differential equation for the given data of initial investment that increases each year at a definite pace
Enter the differential equation
To find the amount after 10 years, enter 0 for tMin and 10 for tMax
Generate a table of values
Use trial and error, to find a closer rate of interest and compare it to the solution of the differential equation
Use the table to estimate the amount in 10 years
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After the Activity

Students solve problems on the exercise page.

Review student results:

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