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 Write-up

Title
I want to be a millionaire!

Problem Statement
If I put \$1.00 in the bank, how many years would it take for me to become a millionaire if my money doubled each year?

Problem setup

This problem involves using the power of exponents.

Plans to Solve/Investigate the Problem

We guessed some different possibilities for this. We then decided to put numbers into an Excel spreadsheet with 3 columns labeled Year, \$ and Powers.

Investigation/Exploration of the Problem

The first number in the "Year" column is 1 for the first year and for every year thereafter, the A rows are labeled up to 21. The first number in the "\$" column is 1 for the one dollar I put in the bank the first year. The first power in the "Powers" column is 1 because in the first year my \$1.00 is just one dollar or one to the first power. We put the following formula in cell B3: =B2*2. We used the black plus cursor to drag the column down so that Excel could calculate the money for each year. We put the following formula in cell C2: =2^(A2-1). The same procedure for using the black plus and dragging down is used for this formula for Excel to calculate the values. The numbers in the "\$" column  and the "Powers" column should be the same. The spreadsheet is as follows:

 Year \$ Powers 1 1 1 2 2 2 3 4 4 4 8 8 5 16 16 6 32 32 7 64 64 8 128 128 9 256 256 10 512 512 11 1024 1024 12 2048 2048 13 4096 4096 14 8192 8192 15 16384 16384 16 32768 32768 17 65536 65536 18 131072 131072 19 262144 262144 20 524288 524288 21 1048576 1048576

Extensions of the Problem

An extension of this problem was the following: If I want to be a millionaire in ten years, how much will my initial deposit in the bank have to be if my money doubled each year? We guessed various numbers and plugged them into Excel using the same formulas. The amount of money needed initially is \$1954.00.

Author & Contact
Pam Joseph
eaglepjo@aol.com

Link(s) to resources, references, lesson plans, and/or other materials