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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.

    Follow the Activity procedures:

  • 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

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