Logistic Model for Population Growth

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This Demonstration illustrates logistic population growth with graphs and a visual representation of the population. As time progresses, note the increase in the number of dots and how the rate of change increases but later decreases. Play the animation for to see the behavior most clearly with discrete time steps. Compare this to exponential growth, presented in an analogous way in a companion Demonstration.

Contributed by: Abby Brown (January 2016)
Open content licensed under CC BY-NC-SA



The logistic model for population as a function of time is based on the differential equation , where you can vary and , which describe the intrinsic rate of growth and the effects of environmental restraints, respectively. The solution of the logistic equation is given by , where and is the initial population.

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