Mathematics

Problem

For a bacterial culture, the mass

y

(in mg) satisfies

\dfrac{dy}{dt}=0.6 y\left(1-\dfrac{y}{1000}\right)

with

y(0)=100

. At what time

t

(in hours) is the instantaneous growth rate

\dfrac{dy}{dt}

greatest? a)

1.8\text{ h}

5.5\text{ h}

3.7\text{ h}

2.5\text{ h}