One model for the spread of a rumor is that the rate of spread is proportional to the product of the fraction y of the population who have heard the rumor and the fraction who have not heard the rumor. (a) write a differential equation that is satisfied by y. (use k for the constant of proportionality.) = (b) solve the differential equation. assume y(0) = c. y = (c) a small town has 2000 inhabitants. at 8 am, 80 people have heard a rumor. by noon half the town has heard it. at what time will 90% of the population have heard the rumor? (do not round k in your calculation. round the final answer to one decimal place.) hours after the beginning