Sociologists recognize a phenomenon called social diffusion, which is the spreading of a piece of information, a technological innovation, or a cultural fad among a population. The members of the population can be divided into two classes: those who have the information and those who do not. In a fixed population whose size is known, it is reasonable to assume that the rate of diffusion is proportional to the number who have the information times the number yet to receive it. If a_n denotes the number of people who have the information in a population of N people after n days, formulate a dynamical system to approximate the change in the number of people in the population who have the information.