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A rumor begins to spread in a population of 10,000 inhabitants thanks to a member of the population hearing it in a neighboring town and beginning to tell the others. Within a week, 1,000 people had heard the rumor. Suppose that the rate at which the rumor spreads is proportional to the square root of the number of residents who have not heard it, and that y(t) is the number of residents who have heard the rumor, t weeks after it started. the propagation. (a) State the differential equation and the conditions that allow finding the number of inhabitants who know the rumor at time t. (b) Determine the number of inhabitants y(t) who have heard the rumor t weeks after it started. (c) 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 a member of the population hearing it in a neighboring town and beginning to tell the others. Within a week, 1,000 people had heard the rumor. Suppose that the rate at which the rumor spreads is proportional to the square root of the number of residents who have not heard it, and that y(t) is the number of residents who have heard the rumor, t weeks after it started. the propagation. (a) State the differential equation and the conditions that allow finding the number of inhabitants who know the rumor at time t. (b) Determine the number of inhabitants y(t) who have heard the rumor t weeks after it started. (c) In approximately how many weeks is it expected that 6400 inhabitants will have heard the rumor?

Algebra & Trigonometry with Analytic Geometry
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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A rumor begins to spread in a population of 10,000 inhabitants thanks to a member of the population hearing it in a neighboring town and beginning to tell the others. Within a week, 1,000 people had heard the rumor. Suppose that the rate at which the rumor spreads is proportional to the square root of the number of residents who have not heard it, and that y(t) is the number of residents who have heard the rumor, t weeks after it started. the propagation. (a) State the differential equation and the conditions that allow finding the number of inhabitants who know the rumor at time t. (b) Determine the number of inhabitants y(t) who have heard the rumor t weeks after it started. (c) In approximately how many weeks is it expected that 6400 inhabitants will have heard the rumor?
Transcribed Image Text:A rumor begins to spread in a population of 10,000 inhabitants thanks to a member of the population hearing it in a neighboring town and beginning to tell the others. Within a week, 1,000 people had heard the rumor. Suppose that the rate at which the rumor spreads is proportional to the square root of the number of residents who have not heard it, and that y(t) is the number of residents who have heard the rumor, t weeks after it started. the propagation. (a) State the differential equation and the conditions that allow finding the number of inhabitants who know the rumor at time t. (b) Determine the number of inhabitants y(t) who have heard the rumor t weeks after it started. (c) In approximately how many weeks is it expected that 6400 inhabitants will have heard the rumor?
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