Question: 13. + 2/3 points | Previous Answers bert An My Notes One model for the spread of a rumor is that the rate of spread

13. + 2/3 points | Previous Answers bert An My Notes 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 Abhisingh who have heard the rumor and the fraction who have not heard the rumor. 2,742 anisv (a) Write a differential equation that is satisfied by y. (Use k for the constant of proportionality. ) dy dt ky( 1 -y) (b) Solve the differential equation. (Let y(0) = yo.) J(0) y(0) + (1-y(0))e-Ri ( c) A small town has 2000 inhabitants. At 8 AM, 160 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. ) 7.6 hours after 8 AM Need Help? Read It Watch It Talk to a Tutor Submit Answer Save Progress

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