A lake is initially stocked with 100 fishes and 1000 zooplanktons on w

Question

A lake is initially stocked with 100 fishes and 1000 zooplanktons on which the fishes prey. There is ample food for the zooplanktons. Because fishes prey on zooplanktons the population of fishes will increase at a rate proportional to the number of encounters between the species. Fishes will also die at a rate

proportional to the fish population. Also fishing is permitted at the rate of $\frac{1}{5}th$ of the existing population at any time. Zooplanktons multiply at a rate proportional to the population and die off at a rate proportional to the number of encounters between the two species. Model this situation.

18 Feb 2025

Answer :

Word Count : 285

This situation can be modeled using a system of differential equations representing the predator-prey dynamics, incorporating natural growth, predation, fishing, and death rates. --- ### Step 1: Define Variables Let: - $ F(t) $ be the fish population at time $ t $. - $ Z(t) $ be the zooplankton population at time $ t $. - _________ ____ __________ _______ _________ ___ ________ _____ __________ _______.
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