Arumor spreads through a school. let y(t) be the fraction of the population that has heard the rumor at time t and assume that the rate at which the rumor spreads is proportional to the product of the fraction y of the population that has heard the rumor and the fraction 1−y that has not yet heard the rumor.

the school has 1000 students in total. at 8 a. m., 95 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?