Session 7, Part B:
Exponential Growth (40 minutes)

In This Part: A Salary Situation | Population Growth

Suppose you are given two different options for salary at a temporary job. Note 5

 Plan A: You can earn \$2,000 each week, or Plan B: You can earn 1 penny the first week, 2 pennies the next week, 4 pennies the next week, and so on, doubling your salary each week.

The job lasts 25 weeks, and your goal is to earn the largest total salary for the 25 weeks.

Problem B1

Which salary plan would you choose and why? Write down your initial reaction.

 Problem B2 Use a spreadsheet or some other method to figure out which salary plan is better.

 When using a spreadsheet, create three columns, one for the week number, one for plan A, and one for plan B. When creating the rule for plan B, remember that the salary is doubling each week, and that the first week's salary is one penny, not one dollar.    Close Tip When using a spreadsheet, create three columns, one for the week number, one for plan A, and one for plan B. When creating the rule for plan B, remember that the salary is doubling each week, and that the first week's salary is one penny, not one dollar.

 Problem B3 Are you surprised that the second salary grew so rapidly? Use the spreadsheet to determine how much money you would make from plan B in 40 weeks.

 To make a column wider, click and hold down on the right edge of the column heading letter, then drag the mouse to the right.   Close Tip To make a column wider, click and hold down on the right edge of the column heading letter, then drag the mouse to the right.

 Video Segment In this video segment, on screen participants discuss the differences between salary plans A and B in Problems B1 and B2 above. In particular, they explore the differences between linear and exponential functions. Watch this segment after you have worked on Problems B1 and B2. If you get stuck, you can watch the video segment to help you. Describe the difference in the ways salary plans A and B grow. Which one is a proportional change, and which is an absolute change? For more on this, see Session 4, Part A You can find this segment on the session video, approximately 7 minutes and 51 seconds after the Annenberg Media logo.

 Session 7: Index | Notes | Solutions | Video