Explanation Use the general solution of the logistic equation and use the initial conditions to obtain the value of the constants. Then determine the time, when 90 % of the students will have heard the rumor. Given: A rumor spreads through a school with 1000 students. At 8 A M , 80 students have heard the rumor and by noon, half of the school has heard the rumor. Calculation: y ' ( t ) is the rate at which the rumor is spreading in percentage of the population per day. Considering k is proportionality constant, we have y ' ( t ) = d y d t = k y ( 1 − y ) and hence the solution will be y ( t ) = 1 1 − e − k t / C The initial condition , y ( 0 ) = 0.08 is used to determine the value of the constant. 8 100 = 1 1 − 1 C = > C = − 2 23 Therefore, the value of the solution y ( t ) = 2 2 + 23 e − k t In 4 hours, the rumor spreads to half of the school therefore, y ( 4 ) = 0...

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 10.4, Problem 9E

To determine

When $90 %$ of the students will have heard the rumor using the logistic model.

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Chapter 10.4, Problem 8E

Chapter 10.4, Problem 10E

Chapter 10 Solutions

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