A bacteria culture follows the differential equation

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

Problem

\dfrac{dy}{dt}=k y\,(1200-y)

, where

k>0

and

y

is measured in cells. At which of the following population sizes is the culture increasing at the greatest instantaneous rate? (a)

y = 900

(b)

y = 300

(c)

y = 600

(d)

y = 1200