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Computer Laboratory


Applications of Differential Equations

Population Dynamics

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Your combined plot should have looked like this:

Show[uscensusplot, usverhulstfitplot]

Best Verhulst Fit Comparison

Well our best-fitting Verhulst model is by far the best fit for the census data that we have seen so far. It isn't perfect, but we can't really expect perfection when modeling population data.

Remember that we used our original Malthus and Verhulst models to predict the US population in 2050, which the U.S. Census Bureau predicts will be 398 million. Neither model did particularly well, though the Verhulst model was better. Now that we've discovered the FindFit command, let's see how well our best-fitting Malthus and Verhulst models do the job. Issue the following two commands in separate cells:

usmalthusfit /. t -> 2050
usverhulstfit /. t -> 2050

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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