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Applications of Differential Equations

Population Dynamics

(continued from last page...)

Your command should have produced this result:

malthus/.t->0
Malthus at 0

This new result seems almost as silly as FindFit's earlier estimate of 0. In fact how can there possibly have been this many people, as you can't have a fraction of a person like this? Well there are two reasons this is better than before. First, at least a non-zero value of p0 has the potential to grow beyond 0. Second, the model we're creating is not going to be used to esimate populations back at the year zero. Maybe the model we'll produce if we use this weird value for p0 will do a good job in the range of t-values we're interested in. At least we can give it a try.

So to summarize, we're now going to try using FindFit again, but this time we will suggest that it start looking for a value of p0 near 10-9, and a value of k near 0.02. Here is the command we'll need to do this:

FindFit[uscensus, usmalthusfit, {{p0, 10^-9}, {k, .02}}, t]

Let's go see what you should have gotten...


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ODE Laboratories: A Sabbatical Project by Christopher A. Barker

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