Biology — Population Growth Models
Exponential and logistic growth with the carrying-capacity solution.
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\frac{dN}{dt} = rN
N(t) = N_0 e^{rt}
\frac{dN}{dt} = rN\left(1 - \frac{N}{K}\right)
N(t) = \frac{K}{1 + \left(\frac{K - N_0}{N_0}\right)e^{-rt}}