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.) dy (b) Solve the differential equation. Assume yto) - c c+l-C C A small town has 500 inhabitants. At 8 AM, 120 people have heard a rumor. By in your calculation. Round the final answer to one decimal place.) noon half the town has heard it. At what time will 90% of the population have heard the rumor? (Do not round k hours after the beginning Submit Anawer Save Progress Practice Another Version