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) = n₀.

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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