Models & Qualitative Behavior · Superchallenge problem

A population obeys $P' = \dfrac12P\left(1 - \dfrac{P}{1000}\right)$ with $P(0) = 250$. Its "shortfall" at time $t$ is $1000 - P(t)$. Compute the total accumulated shortfall $\displaystyle\int_0^\infty \left(1000 - P(t)\right)dt$. Give an exact answer.