Mathematics

Problem

A population satisfies

\frac{dP}{dt}=0.20P

for

0\le t\le 1\,\text{yr}

and

\frac{dP}{dt}=0.60P

for

t>1\,\text{yr}

. If

P(0)=500

, determine the exact time

t>0

(in years) at which

P(t)=1500