A population satisfies

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

Problem

A population

P

satisfies

\displaystyle \frac{dP}{dt}=0.2P\,(120-P)

, where

t

is measured in years and

P

in hundreds of individuals. At which population size is the instantaneous growth rate

\frac{dP}{dt}

greatest? (a)

120

(b)

90

(c)

60

(d)

30