One model for the spread of a rumor is that the rate of spread is proportional to the product of the fraction y of the population who have heard the rumor and the fraction who have not heard the rumor.(a) Write a differential equation that is satisfied by y. (Use k for the constant of proportionality.)dydt = (b) Solve the differential equation. (Lety(0) = y0.) (c) A small town has 3500 inhabitants. At 8 AM, 280 people have heard a rumor. By noon half the town has heard it. At what time will 90% of the population have heard the rumor? (Do not round k in your calculation. Round your final answer to one decimal place.)hours after 8 AM

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Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.7: Applications

Problem 13EQ

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One model for the spread of a rumor is that the rate of spread is proportional to the product of the fraction y of the population who have heard the rumor and the fraction who have not heard the rumor.

(a) Write a differential equation that is satisfied by y. (Use k for the constant of proportionality.)

(b) Solve the differential equation. (Let

y(0) = y₀.)

(c) A small town has 3500 inhabitants. At 8 AM, 280 people have heard a rumor. By noon half the town has heard it. At what time will 90% of the population have heard the rumor? (Do not round k in your calculation. Round your final answer to one decimal place.)
hours after 8 AM

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