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
