A fish population is modeled by the logistic equation

MATHEMATICS · Subjective · AP · Calculus BC · Differential Equations · Differential Equations

Problem

A fish population is modeled by the logistic equation dydt=0.3 y (500−y)\dfrac{dy}{dt}=0.3\,y\,(500-y), where yy is the number of fish and tt is measured in days. Determine (i) the population size at which the growth rate is maximal and (ii) the corresponding instantaneous growth rate (in fish per day).

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