Arumor spreads through a school. let y(t)y(t) be the fraction of the population that has heard the rumor at time tt and assume that the rate at which the rumor spreads is proportional to the product of the fraction yy of the population that has heard the rumor and the fraction 1−y1−y that has not yet heard the rumor. the school has 1000 students in total. at 8 a. m., 100 students have heard the rumor, and by noon, half the school has heard it. using the logistic model explained above, determine how much time passes before 90% of the students will have heard the rumor. 90% of the students have heard the rumor after about hours.