A town’s population obeys

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

Problem

\dfrac{dy}{dt}=0.02\,y\,(1000-y)

, where

y

is the population and

t

is measured in months. At

t=0

, the population is

y=600

. Indicate whether the instantaneous growth rate is increasing or decreasing at

t=0

, and state whether the population has already passed the point of fastest growth. Give a brief justification.