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WOLFRAM|DEMONSTRATIONS PROJECT

A Model for Population Growth

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initial population
y
0
0.1
growth rate r
0.15
carrying capacity M
4
This Demonstration models population growth over time given the initial population, the growth rate, and the carrying capacity in the biome. The carrying capacity depends on limiting factors that may involve, among other things, the amount of biomass available to the population, predation, and environmental stresses. The model can be represented by the equation
y
t
=M/(1+(M/
y
0
-1)exp(-rMt))
, where
y
is the size of the popuation,
t
is time,
M
is the carrying capacity, and
r
is the growth rate. In all cases, a constant, steady state population is eventually reached.
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