Question

Suppose that news spreads through a city of fixed size of 900000 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.dy/dt = k ( what ) , where k is the proportionality constantb.) 8 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) = what

Answer 1

Answer:

The relation is $ln(\frac{900000}{900000 - y(t)} ) = kt$

Step-by-step explanation:

Here we have

$\frac{dy(t)}{dt} =k(900000-y(t))$

Integrating we get

-ln(900000 - y(t)) = kt + C

With initial condition y(0) = 0 we get

C =  -ln(900000)

Therefore,

$ln(\frac{900000}{900000 - y(t)} ) = kt$