Let Q(t) denote the number of people in a city of population N₀ who have been infected with a certain disease t days after the beginning of an epidemic. Studies indicate that the rate R(Q) at which an epidemic spreads is jointly proportional to the number of people who have contracted the disease and the number who have not, so R(Q) = kQ(N₀ − Q). Sketch the graph of the rate function, and interpret your graph. In particular, what is the significance of the highest point on the graph of R(Q)?