Contextual Applications of Differentiation · Challenge problem

A rumor spreads through a population of $500$ people according to $N(t)=\dfrac{500}{1+99e^{-0.5t}}$, where $N(t)$ is the number who have heard it after $t$ days. Find the rate, in people per day, at which the rumor is spreading at the moment exactly half the population has heard it.