Question

The per capita growth rate of many species varies temporally for
a variety of reasons, including seasonality and habitat
destruction. Suppose n(t) represents the population size at time
*t*, where *n* is measured in individuals and
*t* is measured in years. Solve the following differential
equation.

Habitat destruction is modeled as

n' = (r − at)n n(0) =
n_{0}.

Here the per capita growth rate declines over time, going from positive to negative. It is modeled by the function r − at.

n(t) = ?

Describe the predicted population dynamic.

The population size initially increase, reaches a maximum, then decreases, approaching ? in the long run. Thus, the population goes extinct.

Answer #1

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