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Differential Equationsmedium
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A population N(t)N(t)N(t) grows according to the logistic model dNdt=0.2N(1−N500)\frac{dN}{dt} = 0.2N(1 - \frac{N}{500})dtdN​=0.2N(1−500N​). If N(0)=100N(0) = 100N(0)=100, what is the carrying capacity of the population?