Who Wants to Be a Millionaire II

Last week's application dealt with a mathematical situation involving the winnings board on the game show Who Wants to Be a Millionaire? The question was whether there is a best fitting curve that fits the numbers fairly well.

We just kind of left it right there. Again, I apologize for doing this in Euros or what ever those numbers are. I guess that just gives another opportunity to do the project in dollars.

I used a website http://www.had2know.com/academics/regression-calculator-statistics-best-fit.html. It allowed you to input ordered pairs and then would give you four answers: Linear, Exponential, Power, and Logarithmic. The are other websites that have even more options.A teacher could get a lot of mileage out of this. Students could take guesses at which of the four would be best and which would be worst, and what the winning equation might look like. Enough suspense. The equations the website came up with are as follows:

Linear: y = 42877.1492x-209477.1429
                    Correlation:  0.6949

Exponential:  y = 41.5145(1.9468^x)
                    Correlation:  0.9992                  

Power:   y = 11.9805(x^3.5337)
                     Correlation:  0.9267                  

Logarithmic: y = -202534+180689.7131lnx
                      Correlation:  0.512

The winner? Judging by the correlations, the exponential equation, although the power equation wasn't bad. The others, fairly bad.

Students could graph the original 15 ordered pairs along with these four equations for some conformation.