Assume That the Rat Population in a Certain Urban Area $P ( t ) = \frac { 20 } { 1 + 9 e ^ { - 0.31 t } }$

Essay

Assume that the rat population in a certain urban area behaves according to the logistic growth function $P ( t ) = \frac { 20 } { 1 + 9 e ^ { - 0.31 t } }$ where $P$ is the number of rats in the hundreds, and $t$ is measured in months.(a) Find the initial rat population.(b) Find the rat population after $1$ month.(c) After how many months will the rat population triple from its initial size?