A rumor spreads through a small town. Let y(t) be the fraction of the population that has heard the rumor at time t and assumethat the rate at which the rumor spreads is proportional to the product of the fraction y of the population that has heard the rumorand the fraction 1 – y that has not yet heard the rumor.Write the differential equation satisfied by y in terms of a proportionality factor k.(Express numbers in exact form. Use symbolic notation and fractions where needed.)y (t) =Find k (in units of day-), assuming that 15% of the population knows the rumor at t = 0 and 35% knows it at t = 2 days.(Express numbers in exact form. Use symbolic notation and fractions where needed.)k =days-1

y denotes the fraction of population who have heard the rumour then 1 minus y represents the…

Answered: A rumor spreads through a small town.…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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An ice cream shop estimates that the revenue (in dollars) from the sale of x cones is given by R(x)= 11,000ln(0.02x+1). Use the differential to approximate the change in revenue from the sale of one more ice cream cone, if 70 cones have already been sold.
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According to the U.S. Census Bureau, the population of the United States in 2008 was 304 million people. In addition, the population of the United States was growing at a rate of 1.1% per year. Assuming this growth rate continues, the model t – 2008 P(t) = 304 · (1.011)* represents the population P (in millions of people) in year t. According to the model, when will the population be 366 million people? Be sure to round your answer to the nearest whole year. Year
A virus spreads by contact and if you get infected you stay contagious. In an isolated population with P persons (no-one dies or are born) the rate of infection at time t (in months after 1/1 2020) is proportional to the product of 1. the number y(t) that are infected, 2. the number that are not infected 3. eat where a is a negative number depending on disease preventive measures. One tenth of the population is infected 1/1-2020. (a) Write out the differential equation y(t) must satisfy and solve it (call the proportionality constant k and remember to explain each step of your solution carefully. Are there for instance any constant solutions?). (b) Find a relation between L = lim->00 y(t), a, Pand k. What can you say about L when a is very small? What can you say about L when a is very big?
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