The rate of growth of a bacterial culture is given by

MATHEMATICS · Subjective · AP · Calculus BC · Differential Equations · Differential Equations

Problem

The rate of growth of a bacterial culture is given by dNdt=0.4 N ⁣(1−N1000)\dfrac{dN}{dt}=0.4\,N\!\Bigl(1-\dfrac{N}{1000}\Bigr), where NN is the number of bacteria. Determine the population size at which the growth rate is greatest.

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