A substance amount changes according to with initial condition

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

Problem

A substance amount

y(t)

changes according to

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

with initial condition

y(0)=20

. Determine the value approached by

y(t)

t\to\infty

and briefly justify your answer using the sign of

\dfrac{dy}{dt}

for values of

y

below and above that limit.