Mathematics & Science Learning Center
Computer Laboratory

Applications of Differential Equations

Population Dynamics

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As we've seen, there are two popular models for describing population growth, both of which involve first order differential equations. We're going to discuss both models, and compare the results we get with each against reality.

Reality

Census data for the United States has been available since 1790. I've included this census data below as ordered pairs of the form {year, population in millions}, covering through the year 2000:

{{1790, 3.93}, {1800, 5.31}, {1810, 7.24}, {1820, 9.64},
{1830, 12.87}, {1840, 17.07}, {1850, 23.19}, {1860, 31.44},
{1870, 39.83}, {1880, 50.16}, {1890, 62.95}, {1900, 75.99},
{1910, 91.97}, {1920, 105.71}, {1930, 122.78}, {1940, 131.67},
{1950, 151.33}, {1960, 179.32}, {1970, 203.21}, {1980, 226.50},
{1990, 248.71}, {2000, 281.42}}

Notice that the list is in Mathematica matrix form, so you can "cheat" by grabbing the data and moving it over to Mathematica using the copy and paste abilities of your computer.

Welcome back. That should have been fairly painless. Moving on...

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.