Repeat Exercise 19 using the Gompertz growth law,

for constants k and a, with a = 0.1.

Exercise 19

The equation developed in the text for the spread of an epidemic also can be used to describe diffusion of information. In a population of size N, let y be the number who have heard a particular piece of information. Then

for a positive constant k. Use this model in Exercises.

A rumor spreads at a rate proportional to the product of the number of people who have heard it and the number who have not heard it. Assume that 3 people in an office with 45 employees heard the rumor initially, and 12 people have heard it 3 days later.
(a) Write an equation for the number, y, of people who have heard the rumor in t days.
(b) When will 30 employees have heard the rumor?

dy dt kye-at,