Again consider the spreading of a rumor (see Problem 13 in this section), but now assume...

Again consider the spreading of a rumor (see Problem 13 in this section), but now assume a company with 2000 employees. The rumor concerns the number of mandatory terminations that this company must absorb. Based on the model presented in Problem 13, build a model for the company with the following rumor growth rates to determine the number who have heard the rumor after 1 week.

a. k = 0.25

b. k = 0.025

c. k = 0.0025

d. k = 0.00025

e. List some ways of controlling the growth rate.

REFERENCE:

13. Consider the spreading of a rumor through a company of 1000 employees, allworking in the same building.We assume that the spreading of a rumor is similar to the spreading of a contagious disease (see Example 3, Section 1.2) in that the number of people hearing the rumor each day is proportional to the product of the number who have heard the rumor previously and the number who have not heard the rumor. This is given by

where k is a parameter that depends on how fast the rumor spreads and n is the number of days. Assume k = 0.001 and further assume that four people initially have heard the rumor. How soon will all 1000 employees have heard the rumor?