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12.  Pay Days Challenge:
 Exploring patterns of growth using a spreadsheet

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	SREB Readiness Indicator Understand and represent functions algebraically and graphically. > Additional indicators
	Skills Explore non-linear functions Explore rates of change Create tables and graphs of functions
	Figure 1: Table of accumulated cash (Click to enlarge)

Overview

The Pay Days Challenge, a new twist on the classic "penny deal," gives students an opportunity to use a spreadsheet (Figure 1) to explore exponential and linear growth patterns. The problem asks a simple question: Would you rather receive (1) one penny on the first day of the month, two pennies the second, four pennies the third and so on, each day doubling the previous day's amount until the last day of the month? or (2) one million dollars on each Friday of the month. The investigation of the problem can lead to a lively discussion and typically produces surprising discoveries about recursive patterns and exponential doubling.

The Value of This Technology

A spreadsheet (e.g., Microsoft Excel or the spreadsheet component in AppleWorks) is a useful tool for addressing this kind of challenge. Using the spreadsheet to display the calculated value of the accumulated cash throughout the month, students can organize their approach to the problem, identify key factors affecting their answers, and graphically represent the patterns of growth involved in the problem. With the addition of basic formulas and the graphing capabilities of the spreadsheet, students can conduct a more extensive analysis of the information than they could if they were using pencil and paper.

Look in the Classroom

Having spent some time studying linear functions, Ms. Gojack's students are ready to investigate non-linear patterns and expand their understanding of functions.
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