The logistic curve is the graph of the function a f(x) = 1+ be-rx where a, b, and r are suitable parameters. This function may describe, for example, the initial rapid growth of a population, followed by a slowdown of the growth as resources become sparse. Since e¯™ª tends to zero as æ tends to infinity f(x) approaches a as æ tends to infinity, and at a = equals 0 the initial population a f(0) 1+b The rate r is the usual growth rate that would prevail indefinitely in the presence of unlimited resources. Suppose a = 4200, b = 10, and r = 0.01. Then the initial population is | and as time goes on the population approaches but never quite reaches

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