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(Step-by-Step) Suppose that a fish population P(t) in a lake is modeled by a Malthusian population model with a proportionality constant k = 1 and an initial

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.

\[\frac{dP}{dt}=P,\,\,P\left( 0 \right)=10\] (3)
  1. 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 \(t\ge 0\).
  2. Will the population be depleted from the lake at any time?

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