Future Payoffs

This is an excellent opportunity for the students to submit early writing samples. The students don't seem to mind since they have a good understanding (or at least they think they do) of what they are writing about, and each group's paper is personalized.

The nature of the problem requires the use of groups. So, if you haven't found a nice group problem to get the class going, this is a good problem to try.

This problem provides a memorable experience with several important concepts from calculus: velocity is the derivative of position, the derivative can be graphically interpreted as slope. And lesser known, that antidifferentiation tends to smooth data or conversely, that differentiation of real data tends to result in very complicated curves.

This is fun for the instructor to grade.