A rumor begins to spread in a population of 10,000 inhabitants thanks to the fact that a member of the population heard it in a neighboring village and began to tell others about it. After a week 1,000 people had heard the rumor. Assume that the speed at which it propagates the rumor is proportional to the square root of the number of inhabitants who have not heard it and that y(t) is the number of inhabitants who have heard the rumor, t weeks after the start of the spread. (Explain extensively) (a) State the differential equation and the conditions that allow finding the number of inhabitants who know the rumor at time t. (b) Determine the number of inhabitants y(t) who have heard the rumor t weeks after has started. (c) In approximately how many weeks is it expected that 6400 inhabitants will have heard the rumor?