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Math Help - Application problem involving indefinite integrals

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    Application problem involving indefinite integrals

    Wite C(t) for the amount the U.S. military spent on personel in year t, where t is measured in years since 2000. The rate of increase of C(t) was about $3.7 billion per year in 2000 and was projected to decrease to $3 billion per year in 2007.

    Find a linear model for the rate of change C'(t)
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    Quote Originally Posted by Kenneth View Post
    Wite C(t) for the amount the U.S. military spent on personel in year t, where t is measured in years since 2000. The rate of increase of C(t) was about $3.7 billion per year in 2000 and was projected to decrease to $3 billion per year in 2007.

    Find a linear model for the rate of change C'(t)
    we have C'(0) = 3.7 billion and C'(7) = 3 billion

    now we know C'(t) is linear, so let's find it's slope:

    using (x1,y1) = (2000, 3.7 b) and (x2, y2) = (2007, 3 b)

    m = change in C(t)/change in time
    = (3b - 3.7b)/(2007 - 2000)
    = 0.7/-7
    = -1/10 billion/yr

    so we have C'(t) = (-1/10)t + 3.7 billion .........where b is the y-intercept
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