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Applications of Differential Equations

Population Dynamics

(continued from last page...)

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...


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ODE Laboratories: A Sabbatical Project by Christopher A. Barker

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