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...

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ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 10.3, Problem 9E

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Chapter 10.3, Problem 8E

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

Solution Summary: The author calculates the rate at which the rumor is spreading in percentage of the population per day using the logistic model.

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

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

Solution Summary: The author calculates the rate at which the rumor is spreading in percentage of the population per day using the logistic model.

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

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