Consider a fish population (in individuals) that satisfies

MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

Consider a fish population N(t)N(t) (in individuals) that satisfies dNdt=0.08N (1000−N)\displaystyle \frac{dN}{dt}=0.08N\,(1000-N). The instantaneous growth rate is greatest when N=500N=500. What is the smaller of the two population sizes at which the instantaneous growth rate equals one–half of its maximum value? (a) 250250 individuals (b) Approximately 146146 individuals (c) 500500 individuals (d) Approximately 854854 individuals

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