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3. (4 points) Sociologists recognize a phenomenon called social diffusion, which is the spreading of a piece of information, technological innovation, or 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. Sociologists often assume that the rate at witch information spread is proportional to the number who have the information and the number who do not. Suppose y(t) denotes the number of individuals who have the information within t time units in a population of N people. (a) Find a mathematical model for social diffusion. (b) Find the general solution to the model found in (a)