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AP Calculus BC/Unit 7: Differential Equations
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Time of Maximum Logistic Growth

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The growth of a population $P(t)$ is modeled by the differential equation dPdt=0.2P(1−PN) \frac{dP}{dt} = 0.2P\left(1 - \frac{P}{N}\right) with the initial condition $P(0) = \frac{N}{8}$. At what time $t$ is the population increasing most rapidly?

A

t=ln⁡(2)0.2t = \frac{\ln(2)}{0.2}

B

t=ln⁡(7)0.2t = \frac{\ln(7)}{0.2}

C

t=5ln⁡(3)0.2t = \frac{5\ln(3)}{0.2}

D

t=ln⁡(4)0.2t = \frac{\ln(4)}{0.2}

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