For the logistic differential equation

MATHEMATICS · Single correct · AP · Calculus AB · Differential Equations · Differential Equations

Problem

For the logistic differential equation dydt=0.08 y(30−y)\dfrac{dy}{dt}=0.08\,y(30-y), the rate of change attains its maximum value when y=15y=15. At which of the following population sizes is the instantaneous rate of change exactly one–half of this maximum? (a) Approximately 1010 or 2020 (b) Approximately 7.57.5 or 22.522.5 (c) Approximately 4.44.4 or 25.625.6 (d) Approximately 1212 or 1818

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