Write a differential equation that is satisfied by y. Solve the differential equation. and part c.) as well

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 satised by y. (Use k for the constant of proportionality.) E1 = dt (b) Solve the differential equation. (Let y(0) = yo.) (c) A small town has 4000 inhabitants. At 8 AM, 320 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 your nal answer to one decimal place.) hours after 8 AM