I like the copier problem (as I understand it--you showed them the final version as well as the video--yes?). I like it _because_ it's an example of something that's clearly geometric series growth. It's a tricky, thought provoking problem, but with enough concrete background to make the math understandable. One of the ways context is good in math is because you learn how to use math to model the world around you. Another way context is good in math is because the context gives you intuition for the math and why it works the way it works--this seems to me to be a really nice problem of the second kind.

Population growth is interesting in the other way. Population growth is tricky because it isn't particularly exponential over the short term (say 50 years) because there's so much variability (it's not linear--is it exponential? quadratic? what?). It's more exponential looking over the long term. We don't really get the exponential growth model from looking at the numbers and trying to fit a graph to it, we really get exponential growth by thinking about what the factors are that influence population growth, and the simplest of those is that the number of people born depends on the number of people alive at the time--geometric! All of those other factors (war, disease, wealth) mess up the short term predictability of population growth, but over the very long term, that geometric growth tends to dominate. Anyway, my point is that getting an exponential growth model is as much reasoning from the biology as from the math. I find this a very cool insight about mathematical modeling--that it's about noticing physical or geometric relationships and figuring out how to use math to describe them. I think I first realized this about the function for light intensity as you move further from the light source--that's a very cool bit of mathematical thinking (trivial for Isaac Newton, but not something that comes naturally for your average person).