A fish population (in hundreds) in a secluded lake satisfies

MATHEMATICS · Single correct · AP · Calculus BC · Differential Equations · Differential Equations

Problem

A fish population PP (in hundreds) in a secluded lake satisfies dPdt=0.08 P (500−P)\dfrac{dP}{dt}=0.08\,P\,(500-P), where tt is measured in months. At what population size is the instantaneous growth rate dPdt\dfrac{dP}{dt} greatest? (a) 333333 (b) 500500 (c) 250250 (d) 125125

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