Mathematics

Mathematics

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)

as

t\to\infty

and briefly justify your answer using the sign of

\dfrac{dy}{dt}

for values of

y

below and above that limit.

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