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Logistic Growth Curve

The Population Growth law which arises frequently in biology and is given by the differential equation

{dN\over dt}={r(K-N)\over K},
\end{displaymath} (1)

where $r$ is the Malthusian Parameter and $K$ is the so-called Carrying Capacity (i.e., the maximum sustainable population). Rearranging and integrating both sides gives
\int_{N_0}^N {dN\over K-N}={r\over K}\int_0^t dt
\end{displaymath} (2)

\ln\left({N_0-K\over N-K}\right)={r\over K}t
\end{displaymath} (3)

\end{displaymath} (4)

The curve

y={a\over 1+bq^x}
\end{displaymath} (5)

is sometimes also known as the logical curve.

See also Gompertz Curve, Life Expectancy, Logistic Equation, Makeham Curve, Malthusian Parameter, Population Growth

© 1996-9 Eric W. Weisstein