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Math Help - At a loss - finding the formula

  1. #1
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    Angry At a loss - finding the formula

    There are two parts to this one. I actually plotted and created my own a table to organize the data to find the slope of the linear function. They call this function marginal propensity to consume.
    from the book the table looks like this
    year 1990 1997
    total consumption(C) 3839 5494
    National income(I) 6650 4215

    my table is
    year I C
    1990 6650 3839
    1997 4215 5494
    I plotted I on the X axis and C on the Y.
    I saw the line went from right to left meaning I should find a negative slope
    I subtracted the change in both categories to come up with m= 1655/-2435 or -.67967.
    That is the long answer to part b I believe.

    Part a I am totally at a loss.
    Find the formula for C as a function of I.
    c(i) = i -c ? how does year get input into the formula? Been looking at this for days and still stuck.
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  2. #2
    Super Member Aryth's Avatar
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    You have a point and the slope. You can make an equation as long as it is linear:

    \text{Point 0} = (6650, 3839)

    \text{Slope} = -\frac{1655}{2435}

    Where the point is of the form:

    (I, C(I))

    And:

    y = C(I)

    Now, we use point slope form:

    (y - y_0) = m(I - I_0)

    Now, we plug in what we know:

    (y - 3839) = -\frac{1655}{2435}(I - 6650)

    C(I) - 3839 = -\frac{1655}{2435}I + 4520

    C(I) = -\frac{1655}{2435}I + 8359

    Now, we just try to generate the NEXT point that you have given:

    C(4215) = -\frac{1655}{2435}(4215) + 8359

    C(4215) = -2864.8152 + 8359

    C(4215) = 5494.18 \approx 5494

    Therefore the formula stands.

    There you go.
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  3. #3
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    still shakey

    OK I see I should have pulled up using the point-slope formula.
    I am having trouble seeing (I must be blind).
    where did you come up with 4520?
    I am racking my pea brain to find it. I think I am too old for this stuff.
    Thanks
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  4. #4
    Super Member Aryth's Avatar
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    I got the 4520 from:

    -\frac{1655}{2435}*-6650

    It actually yields 4519 point something, but rounding up doesn't change it's validity by much.
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