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/dt = ?
(b) Solve the differential equation. (Let y(0) = y0.)
(c) A small town has 1500 inhabitants. At 8 AM, 120 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 final answer to one decimal place.)