A rumor spreads among a population of N people at a rate proportional to the product of the number of people who heard the rumor and the number of people who did not hear the rumour. If p denotes the number of people who heard the rumor, which of the following differential equations could be used to model this situation with respect to time t, where k is a positive constant?

**Answer 1**

Ah, the AP folks keep surprising me with their ridiculous problems. Since p is the number of people who listened, the number of people who did not hear is everyone except p, or Np. Since the question mentions one product among these, we expect to see the expression p(Np). This expression only appears in option b, so the answer is b.