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. No one 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 dy = k( dt where k is the proportionality constant. (b.) 8 days after a scandal in City Hall was reported, a poll showed that 400000 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. 00 15 y(t) = Ed E ENG 2021/09/11
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. No one 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 dy = k( dt where k is the proportionality constant. (b.) 8 days after a scandal in City Hall was reported, a poll showed that 400000 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. 00 15 y(t) = Ed E ENG 2021/09/11
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
b
Transcribed Image Text:Suppose that news spreads through a city of fixed size of 800000
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.
No one 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
dy
= k(
),
dt
where k is the proportionality constant.
(b.) 8 days after a scandal in City Hall was reported, a poll showed that 400000
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.
00:15
y(t) =
ENG
9HO 4
2021/09/11
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