Question

Suppose that news spreads through a city of fixed size of 700000 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

Answer 1

Answer:

y'(t) = k(700,000-y(t))  k>0 is the constant of proportionality

y(0) =0

Step-by-step explanation:

(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.

If we suppose that news spreads through a city of fixed size of 700,000 people at a time rate proportional to the number of people who have not heard the news that means  

dy/dt = k(700,000-y(t)) where k is some constant of proportionality.

Since no one has heard the news at first, we have

y(0) = 0 (initial condition)

We can then state the initial value problem as

y'(t) = k(700,000-y(t))

y(0) =0