Chapter 4.4, Problem 187E

It is more likely that the amount of fishing is governed by the current number of fish present, so instead of a constant number of fish being caught, the rate is proportional to the current number of fish present, with proportionality constant k, as

   $P\text{'}=0.4P\left(1-\frac{P}{10000}\right)-kP$

187. Solve this equation, assuming a value of k = 0.05 and an initial condition of 2000 fish.