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...

See similar textbooks

Similar questions

If a cup of coffee has temperature 92°C in a room where the ambient air temperature is 23°C, then, according to Newton's Law of Cooling, the temperature of the coffee after t minutes is T(t) 54 23 + 69e-/ . What is the average temperature of the coffee during the first 36 minutes? average temp = °C
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?
Use the total differential to approximate the quantity. Then use a calculator to approximate the quantity, and give the absolute value of the difference in the two results to four decimal places. √3.09² +3.97² Approximate the quantity using the total differential. √3.09² +3.97² (Type an integer or a decimal. Do not round until the final answer. Then round to four decimal places as needed..) Approximate the quantity using a calculator. √3.09² +3.97² ន (Type an integer or a decimal. Do not round until the final answer. Then round to four decimal places as needed.) Find the absolute value of the difference in the two results above.

Recommended textbooks for you

Calculus: Early Transcendentals

Calculus

ISBN:

9781285741550

Author:

James Stewart

Publisher:

Cengage Learning

Thomas' Calculus (14th Edition)

Calculus

ISBN:

9780134438986

Author:

Joel R. Hass, Christopher E. Heil, Maurice D. Weir

Publisher:

PEARSON

Calculus: Early Transcendentals (3rd Edition)

Calculus

ISBN:

9780134763644

Author:

William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher:

PEARSON

Calculus: Early Transcendentals

Calculus

ISBN:

9781285741550

Author:

James Stewart

Publisher:

Cengage Learning

Thomas' Calculus (14th Edition)

Calculus

ISBN:

9780134438986

Author:

Joel R. Hass, Christopher E. Heil, Maurice D. Weir

Publisher:

PEARSON

Calculus: Early Transcendentals (3rd Edition)

Calculus

ISBN:

9780134763644

Author:

William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher:

PEARSON

Calculus: Early Transcendentals

Calculus

ISBN:

9781319050740

Author:

Jon Rogawski, Colin Adams, Robert Franzosa

Publisher:

W. H. Freeman

Precalculus

Calculus

ISBN:

9780135189405

Author:

Michael Sullivan

Publisher:

PEARSON

Calculus: Early Transcendental Functions

Calculus

ISBN:

9781337552516

Author:

Ron Larson, Bruce H. Edwards

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS