The Gompertz growth law,

for constants k and a, is another model used to describe the growth of an epidemic. Repeat Exercise 15, using this differential equation with a = 0.02.

 Exercise 15

An influenza epidemic spreads at a rate proportional to the product of the number of people infected and the number not yet infected. Assume that 100 people are infected at the beginning of the epidemic in a community of 20,000 people, and 400 are infected 10 days later.
(a) Write an equation for the number of people infected, y, after t days.
(b) When will half the community be infected?

Transcribed Image Text:

dy dt = kye-at,