A rumor spreads through a school. Let y(t) be the fraction of the population that has heard the rumor attime t and assume that the rate at which the rumor spreads is proportional to the product of the fraction y ofthe population that has heard the rumor and the fraction 1-y that has not yet heard the rumor. That is,assumey(t) = ky(1 - y)where k is an unknown constant. The school has 1000 students in total. At 8 a.m., 97 students have heardthe rumor, and by noon, half the school has heard it. Using the logistic model, determine how much timepasses before 90% of the students will have heard the rumor. (Note: Since y(t) denotes a proportion,0 ≤ y(t) ≤ 1 for all t, and y = 1 means 100% of the students know.)90% of the students have heard the rumor after abouthours.

Let y(t) be the fraction of the population that has heard the rumor at time t.The differential…

Answered: A rumor spreads through a school. Let…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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