A biological population satisfies

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

Problem

A biological population satisfies dydt=k y (a−y)\dfrac{dy}{dt}=k\,y\,(a-y). Measurements show that when the population is 5050 individuals, its growth rate is 7575 individuals per month, and when the population reaches 200200 individuals, its growth rate is 00. Which ordered pair (k,a)(k,a) is consistent with these observations? (a) (0.0075,200)(0.0075,200) (b) (0.02,150)(0.02,150) (c) (0.01,200)(0.01,200) (d) (0.015,200)(0.015,200)

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