Water Rumor A rumor about dihydrogen monoxide in the drinking water began to spread one da...

Water Rumor A rumor about dihydrogen monoxide in the drinking water began to spread one day in a city of population 200,000. After one week, 1,000 people had been alarmed by the news. Assume that the rate of increase of the number N of people who have heard the rumor is proportional to the product of those who have heard the rumor and those who have not heard the rumor. Assume that N(0) = 1.

(a) Find an expression for .

(b) Is this a logistic model? Explain.

(c) What are the equilibrium solutions, if any?

(d) Solve for N(t), to find how long it takes for half the population to take notice.

(e) Suppose that at some point the problem is discussed in the newspaper, and some intelligent souls explain that there is no cause for alarm. Create a scenario and set up an IVP to model the spread of a counterrumor.