Calculus: Other Calculus Problems – #28378

Question: Logistic Growth Many populations grow according to the logistic equation

\[\frac{dx}{dt}=rx\left( N-x \right)\]

where r is a constant involving the rate of growth and N is the carrying capacity of the environment, beyond which the population decreases. Show that the graph of x has an inflection point where x = N/2.

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