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Exponential and Logarithmic Functions

Endangered Species: A conservation organization releases 100 animals of an endangered species into a game preserve. The organization believes that the preserve has a carrying capacity of 1000 animals and that the growth of the herd will follow the logistic curve.

where t is measured in months

(a) Use a graphing utility to graph the function. Use the graph to determine the horizontal asymptotes and interpret the meaning of the larger asymptote in the context of the problem.
(b)Estimate the population after 5 months
(c)When will the population reach 500?

Solution Preview

(a) (See attached graph in Chart11918a.xls)
As t approaches -infinity, p(t) approaches zero.
As t approaches +infinity, p(t) approaches 1000.
These describe the two horizontal asymptotes of the function p.
In terms of the problem, the larger asymptote value (1000 as t ...

Solution Summary

Population is modeled using an exponential function. The explanation is detailed.