## Friday, July 20, 2012

### M&Ms and the Population of Afghanistan

In Business Calc, we're currently studying exponential growth and decay.  I'm rather excited about this since it's something we study in College Algebra, too, and I feel--because it's material I've taught before--that I can expand a bit.  I'm learning that it's really, really hard to expand (i.e., go beyond an absolutely dazzling lecture *cough*) when I'm teaching a class for the first time.  I sort of feel like I did my first semester as a TA:  I just hope I don't screw something up too terribly. But--you gotta start somewhere, right?!

Anyway.  Back to exponential growth/decay.  In College Algebra, when we study exponential functions, I have my students model the decay of an M&M population.  I had planned to do this with my Business Calc class as well.  Then Bowman Dickson posted places to find awesome data, which made me want to use data the UN has on the world's populations instead.

The question:  How to relate M&M's to population growth or decay?

The answer:  I'm not entirely sure.  Here's what we did though...

We started out with the M&M project as in College Algebra.  Each team found the exponential regression (in the form y=ab^x) and the r^2 value for their data.  We talked about the meaning of a and b.  Then I asked them to convert their regressions to the form P(t)=P_0e^(kt), which turned out to be very close to the trendlines Excel found (yay!).  We talked about what k would mean if it this were a real population and how it's related to the derivative.

Now the challenge:  I asked them to do the same types of calculations for an actual population, using data from the UN.  They were on their own for this project, which may or may not have been a great idea.  Below is what they had to go off of.  I focused mainly on finding the exponential regression on a TI as well as understanding growth/decay rates.  But there's much, much more to do here (Bowman does a week-long project!).

And here's the project!

Population Growth or Decay Instructions