A fish population grows according to

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

Problem

\dfrac{dy}{dt}=0.05\,y\,(1000-y)

, where

y

is the number of fish. Which statement correctly compares the instantaneous growth rates when

y=200

and when

y=800

? (a) The instantaneous growth rate at

y=200

is less than that at

y=800

, and both rates are positive. (b) The instantaneous growth rates at

y=200

and

y=800

are equal. (c) The instantaneous growth rate at

y=200

is greater than that at

y=800

. (d) The instantaneous growth rate at

y=200

is negative, whereas at

y=800

it is positive.