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
<em>dy/dt = k(700,000-y(t)) </em>where k is some constant of proportionality.
Since no one has heard the news at first, we have
<em>y(0) = 0 (initial condition)
</em>
We can then state the initial value problem as
y'(t) = k(700,000-y(t))
y(0) =0
3(x2+2)-3y
3((2)^2+2) - 3(2/3)
first exponents,
3(4+2) - 3(2/3)
then parenthesese
distribute 3
12 + 6 - 2
18 - 2
16
Plug in what we know:
Find the cube root of both sides:
![\sf~a=\sqrt[3]{2744}](https://tex.z-dn.net/?f=%5Csf~a%3D%5Csqrt%5B3%5D%7B2744%7D)
Simplify:
You want the equation for a line that goes through the data points (0, 248) and (5, 277). The slope is ∆y/∆x = (277-248)/(5-0) = 29/5 = 5.8. The first data point is the y-intercept, so your equation in slope-intercept form is
... y = 5.8x + 248 . . . . . . where y is MWh of generation and x is years since 2007.
_____
∆y is read "delta y". It means "the change in y".
