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Mathematics & Science Learning Center
Computer Laboratory


Applications of Differential Equations

Population Dynamics

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Your attempt to find the best fitting Verhuslt parameters should have gone like this:

FindFit[uscensus, usverhulstfit, {l, k}, t]
FindFit Verhulst First Try

The result for l is not entirely unreasonable, but the k-value is quite ridiculous. l represents the carrying capacity of the environment, and while it appears to be larger than what Mathematica is predicting, it is not wildly wrong. But k is a measure of the population's growth rate, and this cannot possibly be right. It is saying that the US population is growing at around 1,808,950%. We know from our work with Malthus, and also from our previous attempt with Verhulst that a more realistic growth rate is in the ballpark of 2%. So yet again we are going to have to help Mathematica by suggesting where it should look for the values of these parameters. Try FindFit again, this time with the command:

FindFit[uscensus, usverhulstfit, {{l, 10^8}, {k, .02}}, t]

Let's move on and see what you should have gotten...

Compass If you're lost, impatient, want an overview of this laboratory assignment, or maybe even all three, you can click on the compass button on the left to go to the table of contents for this laboratory assignment.

ODE Laboratories: A Sabbatical Project by Christopher A. Barker

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