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(Solved): The rate of change \( \frac{d P}{d t} \) of the number of bears on an island is modeled by the foll ...
The rate of change \( \frac{d P}{d t} \) of the number of bears on an island is modeled by the following differential equation: \[ \frac{d P}{d t}=\frac{1992}{17723} P\left(1-\frac{P}{664}\right) \] At \( t=0 \), the number of bears on the island is 185 and is increasing at a rate of 15 bears per day. At what value of \( P \) is \( P(t) \) growing the fastest?
Expert Answer
Given rate of change of number of bears on an island is dPdt=1,99217,723P(1?P664)=1,99217,723(P?P2664) ddt(dPdt)=1,99217,723ddP(P?P2