Differential Equationsmedium
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A population P(t)P(t) is modeled by the logistic equation dPdt=0.2P(1P1000)\frac{dP}{dt} = 0.2P(1 - \frac{P}{1000}). If the initial population P(0)=500P(0) = 500, what is the value of dPdt\frac{dP}{dt} at t=0t=0?