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recitation1

# recitation1 - 15-100 RECITATION 1 FALL 2007 The growth in a...

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15-100 RECITATION 1 - FALL 2007 The growth in a population can be modeled using the logistic method. In this method, the population growth is limited by various resources (food, shelter) to some carrying capacity. The carrying capacity is the maximum number of a species that can be supported by the region. The increase in population I for one year is given by the equation I = rN K " N K # \$ % & ( where r = the annual growth rate (assuming no limits on population growth) N = the current population size at the beginning of the year K = the carrying capacity of the region For example, if you have an initial herd of N = 100 deer that have an annual growth rate of r = 0.5 (50% increase in one year) in a park that can support K = 500 deer, then the deer will increase in population as follows: N (at start of year) I (increase in population) N (at end of year) 100 40.0 140.0 140.0 50.4 190.4 190.4 58.94784000000001 249.34784000000002 249.34784000000002 62.499574687334395 311.84741468733444 311.84741468733444 58.674897296492894 370.5223119838273 370.5223119838273 47.974372314072994 418.4966842979003 418.4966842979003 34.108867380613724 452.605551678514 452.605551678514 21.450990429044985 474.056542107559 474.056542107559 12.298665938803648 486.35520804636263 486.35520804636263 6.6362156293606365 492.9914236757233 Notice that as the population approaches the carrying capacity, the annual increase begins to slow down so that the species does not become over-populated for the given region.

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