Suppose that news spreads through a city of fixed size of 300000 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 ,
the number of people who have heard the news days after it has
happened.
No one has heard the news at first, so . 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
,
where is the proportionality constant.
(b.) 7 days after a scandal in City Hall was reported, a poll showed that
150000 people have heard the news. Using this information and the differential
equation, solve for the number of people who have heard the news after
days.
You can earn partial credit on this problem.