In its early phase, specifically the period 1984–1990, the AIDS epidemic could be modeled* by the cubic function C(t) = −170.36t³ + 1,707.5t² + 1,998.4t + 4,404.8 for 0 ≤ t ≤ 6 where C is the number of reported cases t years after the base year 1984.

a. Compute and interpret the derivative C'(t).

b. At what rate was the epidemic spreading in the year 1984?

c. At what percentage rate was the epidemic spreading in 1984? In 1990?