A rumor spreads through a small town. Let y(t)be the fraction of the population that has heard the rumor at time t and assume that the rate at which the rumor spreads is proportional to the product of the fraction y of the population that has heard the rumor and the fraction 1-y that has not yet heard the rumor. 1.    Write down the differential equation satisfied by y in terms of a proportionality factor k. 2.   Find k (in units of day-1), assuming that 10% of the population knows the rumor at t=0 and 40% knows it at t=2 days. 3.   Using the assumptions of part (b), determine when 75% of the population will know the rumor.

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