Models & Qualitative Behavior · Superchallenge problem

The solution of the logistic equation $P' = P(1 - P)$ with $P(0) = 2$ (a population above its carrying capacity) decreases toward $1$ as $t \to \infty$. Followed backwards in time, it becomes infinite at some negative time $t_0$. Find $t_0$. Give an exact answer.