Models & Qualitative Behavior · Superchallenge problem

A population follows a logistic model $P' = rP\left(1 - \dfrac{P}{K}\right)$ with unknown $r$ and $K$. It is $200$ at $t = 0$, and its growth rate is at its largest at $t = 5$, when the population is $500$. What is the population at $t = 10$?