I thought about the Who Wants to Be a Millionaire money board as a good math application. I've thought how much pressure it would be to be a contestant. Once you get up to the big money, each step is a big deal. It's tempting to go on, even though you could lose everything.
The relationship clearly isn't linear. If it was, it would make the decision making a lot easier. But what is going on with these numbers? I thought it would be interesting to try to fit an equation to this set of numbers.It might be good to first have students take a shot at it without any help. Most would probably see that it isn't linear. Most in fact would see a two and an exponent would be involved somehow. There could be a pretty even split, though, between 2^x and x^2.
It might help students to graph the values 0 (1,100), (2,200)...
Clearly, some kind of doubling is going on. It goes from 100 to 200. It takes a bit of a detour at 300, then 500, 1,000, 2,000, 4,000, 8,000, 16,000, 32,000, 64,000. Then a bump at 125,000, but then rights itself to the doubling pattern for the last few.
An astute student might think that the relationship is something like 2^x. However, when it doesn't double, it come up a little short of doubling. So, the base value might be a little less than 2.
By the way, you might have noticed that this is not in dollars. It must be the European version and those are pounds or Euros or something. I don't remember what that symbol means. I meant to do the dollar version. I didn't even know there was another. The dollar version has similar, but not identical numbers. This same project could be done with those numbers as well.
Anyway, most students are familiar with the game, so it might be a fun exercise for them. Next week I'll share some final results.
