is this too vague? or something or is this not as simple as i thought just for a 1030 class
There are many ways to develop such a model. For example, one may try to have a linear function and to minimize the square of error for each year. I did this in OpenOffice Calc using LINEST function and got the following line equation: . See the graphs here: .
With more complex models, in fact, any number can be a prediction, say, for 2011. Indeed, given points , , there exists a Lagrange polynomial of degree such that for all .
Well, the number of cicadas went from 20 to 38 (which is almost 40) in 17 years, then went from 38 to 82, which just slightly larger than 80 in 17 years, but in the final 17 years only increased by maybe 3/2 rather than doubling.
Letting N(t) be the number of cicadas t years after 1953 suggests for the first three data points but the last one does not fit.