Question: Suppose that a fish population \(P\left( t \right)\) in a lake is modeled by a Malthusian population model with a proportionality constant k = 1 and an initial population \(P\left( 0 \right)=10\). Time is measured in years.

(a) Adjust the mode to account for the additional assumption that fish is continuously migrating to and out of the lake at a rate of \(20\cos t\) fish per year. Also, determine \(P\left( t \right)\) for all \(t\ge 0\).

(b) Will the population be depleted from the lake at any time?