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
\frac{dy}{dt} = k (),where k is the proportionality constant.
(b) 9 days after a scandal in City Hall was reported, a poll showed that 350000 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) =

(a)

(b)

Step-by-step explanation:

Given: 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.

To find:

(a) a differential equation

(b) number of people who have heard the news after t days

Solution:

(a)

Total number of people in a city = 700000

As y(t) denotes the number of people who have heard the news t days after it has happened

Number of people who have not heard the news = 700000 - y(t)

So, differential equation is

Here, k is the proportionality constant.

(b)

Integrate both sides of the differential equation.

Use

As a poll showed that 350000 people have heard the news 9 days after a scandal in City Hall was reported,  

i think it would be 43 movies that would have to be watched.

step-by-step explanation:

think about it. for the second plan, every month is 8 dollars. 8 x 12= 96. so thats the number for the second plan. now for the first plan, its annual meaning you have to pay 10 dollars every year. so now you have to get an equivalent amount of 86 since 96-10=86. 86 divided by 2 since every movie costs 2$ then you would have to watch 43 movies a year to get the same as the second plan. i really hoped this . have a wonderful day as well!

-10i^2-4i

step-by-step explanation:

evaluate for p=2,q=5i

(2−4)(2+5i)i

(2−4)(2+5i)i

=−10i2−4i