$32 - 34$ Seasonality and habitat destruction The per capita growth rate of many species varies temporally for a variety ofreasons, including seasonality and habitat destruction. Suppose $n ( t )$ represents the population size at time $t ,$ where $n$ ismeasured in individuals and $t$ is measured in years. Solve the differential equation for habitat destruction and describe the predicted population dynamics.
$n ^ { \prime } = e ^ { - t } n \quad n ( 0 ) = n _ { 0 }$
Here the per capita growth rate declines over time, but
always remains positive. It is modeled by the function $e ^ { - t }$ .