For a bacterial culture

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

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}

(b)

5.5\text{ h}

(c)

3.7\text{ h}

(d)

2.5\text{ h}