# Basic mathematical models

• Dec 1st 2010, 09:34 PM
iZac01
Basic mathematical models
SO I have a math problem that I forgot how to do.

I need to develop a mathematical model describing the number of cicadas in a given year.

Year: | 1953 | 1970 | 1987 | 2004
Cicadas: | 20 | 38 | 82 | 127
• Dec 2nd 2010, 01:59 AM
iZac01
is this too vague? or something or is this not as simple as i thought just for a 1030 class
• Dec 2nd 2010, 03:10 AM
mr fantastic
Quote:

Originally Posted by iZac01
SO I have a math problem that I forgot how to do.

I need to develop a mathematical model describing the number of cicadas in a given year.

Year: | 1953 | 1970 | 1987 | 2004
Cicadas: | 20 | 38 | 82 | 127

Plot the points. What model is suggested? Fit the points to that model.
• Dec 2nd 2010, 03:13 AM
emakarov
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: \$\displaystyle y = 2.147x - 4181.2\$. See the graphs here: Attachment 19930.

With more complex models, in fact, any number can be a prediction, say, for 2011. Indeed, given \$\displaystyle n\$ points \$\displaystyle (x_i,y_i)\$, \$\displaystyle i=1,\ldots,n\$, there exists a Lagrange polynomial \$\displaystyle f(x)\$ of degree \$\displaystyle n - 1\$ such that \$\displaystyle f(x_i)=y_i\$ for all \$\displaystyle i=1,\dots,n\$.
• Dec 2nd 2010, 08:18 PM
iZac01
Quote:

Originally Posted by mr fantastic
Plot the points. What model is suggested? Fit the points to that model.

I honestly have no idea though he gave us a hint ( estimate the doubling time )
• Dec 3rd 2010, 12:21 AM
emakarov
I am not sure what "estimate the doubling time" means.
• Dec 3rd 2010, 04:14 AM
HallsofIvy
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 \$\displaystyle 20(2^{t/17}\$ for the first three data points but the last one does not fit.