A bacterial culture satisfies with

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

Problem

A bacterial culture satisfies

\dfrac{dy}{dt}=0.5\,y\,(100-y)

with

y(0)=10

. Measurements show

y(4)=30

. Without solving the differential equation, decide whether the time at which the growth rate is maximal occurs before

t=4

hours, after

t=4

hours, or exactly at

t=4

hours. Briefly explain your reasoning.