uppose that news spreads through a city of fixed size of 200000 people at a time rate proportional to the number of people wh ave not heard the news. a.) Formulate a differential equation and initial condition for y(t), the number of people who have heard the news t days after i appened. loone has heard the news at first, so y(0) = 0. The "time rate of increase in the number of people who have heard the news roportional to the number of people who have not heard the news" translates into the differential equation =k( t-y ), here is the proportionality constant
uppose that news spreads through a city of fixed size of 200000 people at a time rate proportional to the number of people wh ave not heard the news. a.) Formulate a differential equation and initial condition for y(t), the number of people who have heard the news t days after i appened. loone has heard the news at first, so y(0) = 0. The "time rate of increase in the number of people who have heard the news roportional to the number of people who have not heard the news" translates into the differential equation =k( t-y ), here is the proportionality constant
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Please don't provide handwritten solution .......
![Modelling the Spread of News [See Prob. 7.5.30]
Suppose that news spreads through a city of fixed size of 200000 people at a time rate proportional to the number of people who
have not heard the news.
(a.) Formulate a differential equation and initial condition for y(t), the number of people who have heard the news t days after it has
happened.
Noone has heard the news at first, so y(0) = 0. The "time rate of increase in the number of people who have heard the news is
proportional to the number of people who have not heard the news" translates into the differential equation
),
d = k t-y
dt
where k is the proportionality constant.
(b.) 5 days after a scandal in City Hall was reported, a poll showed that 100000 people have heard the news. Using this information
and the differential equation, solve for the number of people who have heard the news after t days.
y(t) =
P-(1-P)*exp(k*5)
⠀
Note: You can earn partial credit on this problem.
You are in the Reduced Scoring Period: All additional work done counts 75% of the original.
Preview My Answers Submit Answers](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa6d25292-7b99-469a-aeb5-35a8f1578cc0%2Fa2056b7c-fc9d-48f4-9321-5e178bd72616%2Fsshtrin_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Modelling the Spread of News [See Prob. 7.5.30]
Suppose that news spreads through a city of fixed size of 200000 people at a time rate proportional to the number of people who
have not heard the news.
(a.) Formulate a differential equation and initial condition for y(t), the number of people who have heard the news t days after it has
happened.
Noone has heard the news at first, so y(0) = 0. The "time rate of increase in the number of people who have heard the news is
proportional to the number of people who have not heard the news" translates into the differential equation
),
d = k t-y
dt
where k is the proportionality constant.
(b.) 5 days after a scandal in City Hall was reported, a poll showed that 100000 people have heard the news. Using this information
and the differential equation, solve for the number of people who have heard the news after t days.
y(t) =
P-(1-P)*exp(k*5)
⠀
Note: You can earn partial credit on this problem.
You are in the Reduced Scoring Period: All additional work done counts 75% of the original.
Preview My Answers Submit Answers
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 2 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
