A rumor begins to spread in a population of 10,000 inhabitants thanks to the fact that a member of the population heard it in a neighboring village and began to tell others about it. After a week 1,000 people had heard the rumor. Assume that the speed at which it propagates the rumor is proportional to the square root of the number of inhabitants who have not heard it and that y(t) is the number of inhabitants who have heard the rumor, t weeks after the start of the spread. (Explain extensively) A) State the differential equation and the conditions that allow finding the number of inhabitants who know the rumor at time t. Also determine the number of inhabitants y(t) who have herd the rumor t weeks after has started and in approximately how many weeks is it expected that 6400 inhabitants will have heard the rumor.

A rumor begins to spread in a population of 10,000 inhabitants thanks to the fact that a member of the population heard it in a neighboring village and began to tell others about it. After a week 1,000 people had heard the rumor. Assume that the speed at which it propagates the rumor is proportional to the square root of the number of inhabitants who have not heard it and that y(t) is the number of inhabitants who have heard the rumor, t weeks after the start of the spread. (Explain extensively) A) State the differential equation and the conditions that allow finding the number of inhabitants who know the rumor at time t. Also determine the number of inhabitants y(t) who have herd the rumor t weeks after has started and in approximately how many weeks is it expected that 6400 inhabitants will have heard the rumor.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 94E

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