# Activities

• • • ##### Subject Area

• Math: PreAlgebra: Nonlinear Functions

• ##### Author 6-8

60 Minutes

• ##### Device
• TI-73 Explorer™
• ##### Other Materials
This is Activity 12 from the EXPLORATIONS Book:
Discovering Mathematics with the TI-73: Activities for Grades 7 And 8

• ##### Report an Issue

A Penny Saved is a Penny Earned

#### Activity Overview

Students investigate exponential growth in powers of 2 and discover patterns in their sums.

#### Before the Activity

• See the attached PDF file for detailed instructions for this activity
• Print pages 111 - 116 from the attached PDF file for your class
• #### During the Activity

Distribute the pages to the class.

• Find if it is better to take a lump sum of a million dollars, or take money, starting with a penny, with the amount doubling every day for 31 days
• Use the constant function on the calculator to constantly double the previous amount
• Use the calculator to compute the pennies paid each day and the cumulative total in dollars
• Generate a list of days, pennies paid, and cumulative total
• Create a scatter plot of cumulative total in dollars versus days
• Adjust the window of the calculator and look at plotted data for 10 days, 15 days, and 30 days
• Enter an equation that describes the graph
• Observe that the graph increases exponentially
• Create a graph for the amount \$1,000,000, observe that it is a straight horizontal line
• Examine the plan that doubles the amount every day and observe that it earns more than a million dollars after 27 days
• #### After the Activity

Students will complete the Worksheet and analyze the results.

Review student results:

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