## Monday, January 21, 2013

### A Variation on Using Powers of 2 to Eliminate Debt

Are you tired of the powers of 2 problems you've seen? Well, most students are not familiar with them, so why not impress another generation while developing their understanding of exponential growth and sharpening their mental math and exponent skills.

The title suggests there is a practical application for this activity, either for our national debt or our personal credit card or mortgage obligations. How you bring this in is all about your personal preference.

We'll start the usual way:

## You receive a penny on January 1, 2013; 2 pennies on January 2nd, 4 on January 3rd, 8 on January fourth and so on.How many dollars will you have accumulated by the end of the month?

To make this a little different why not have your students or children at home use 1 significant digit estimates and do this without pencil and paper!

For example we know 2^5 = 32, therefore 2^ 10 ≈ 1000 or 10^3, so 2^20 ≈ 1,000,000 or 10^6. Continuing, 2^30 ≈ (10^6)•(10^3) = 10^9.
But this is in pennies, so you'd have around 10^7 dollars or \$10M!

So is this a fair estimate of how much would have accumulated by the end of Jan? If not, correct my error(s)!

As a teaching strategy, you could demonstrate one of these procedures first, then ask students to devise another path to 2^30 or
2^31.

So what is our approximate national debt today? First one to find it on your smartphone receives a penny!

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