Answer:
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Step-by-step explanation:
Given
In 1990; Income= $39000
In 2010; Income= $70768
Solving (a): An equation in form of f(x) = ax + b
First, we need to determine the slope, a

Taking y as income and x as year index.
When x = 0; y = 39000
When x = 20; y = 70768
Substitute these values in the above formula



Next, is to determine the formula using:

<em>Considering :When x = 0; y = 39000, we have</em>
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<em>Make y the subject of formula</em>
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<em>Express y as a function of x</em>
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Solving (b): Income in 2005
<em>In 2005, x = 15</em>
So:
becomes


Note that if

, then

, and so we can collapse the system of ODEs into a linear ODE:


which is a pretty standard linear ODE with constant coefficients. We have characteristic equation

so that the characteristic solution is

Now let's suppose the particular solution is

. Then

and so

Thus the general solution for

is

and you can find the solution

by simply differentiating

.
It's suppose to be -18 so I guess no real number....
5) The slope is: 6
6) Answer: y=-1/2x+3
7) Answer: The slope is: -8, the y intercept is: 6
8) Answer: y=8x+30
Have a good day and a hug :D づ◡﹏◡)づ
<span>m = 4a + 2c
a = 25; c = 5
Replace a with 25. Replace c with 5.
Then evaluate the expression.
m = 4 * 25 + 2 * 5
m = 100 + 10
m = 110
Answer: 110 meatballs are needed.</span>