iTunes Song Sales and Exponential Functions

Earlier in the year I was looking for some information about using iPods in the classroom. At the same time I was teaching the exponential functions unit in my grade 12 course. One of the pages I came across was this iTunes Song Sales graph. Despite my excitement for iPods I stopped what I was doing and integrated the data I had found into my class. My thinking was that this is data that students can relate to and hopefully it would keep them interested and help them see how math is used in the 'real world'.

Here's what I had my students do:

a) Describe the shape of the curve.
b) Why does it look the way it does?
c) Model it with a function.
d) Can we expect this trend to continue?
e) If not what can Apple do to increase its revenue. This question led to some interesting discussion about what Apple should be doing in the future (including selling books) before the iPad was announced.

There's not much to it but it just gets students thinking about where exponential functions appear in real life and who might care about them. Next time I might get students to do some research to find their own 'real life' exponential situation.

One of the interesting tangents of this lesson arose when a student asked "Why would anyone buy music when you can just download it for free?". We had a good discussion about why it's important to compensate content creators for the enjoyment of their work. We also talked about Creative Commons and how some creators choose to release their products for free and encourage others to use it or even change it. I love days when I end up teaching more than just math.