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Math Help - Piecewise snowstorm

  1. #1
    Newbie
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    Mar 2010
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    Piecewise snowstorm

    Hey everyone, i have this problem:
    During a 9 hour snowstorm, it snows at a rate of 1 inch per hour for the first 2 hours, at a rate of 2 inches per hour for the next 6, and at a rate of 0.5 per hour for the final hour. Write and graph a piecewise-defined function that gives the depth of the snow during the snowstorm. How many inches of snow accumulated from the storm?

    and so i have gotten to this point so far

    F(x)= 0, if x <0
    = [[x]], if x >0 and x < 2
    = 2[[x]]-2, if x => 2 and x <8

    and i can not figure out the equation for the 4th part of the function, also would like to know if i am on the right track, any help would be much appreciated, thanks!
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  2. #2
    Super Member

    Joined
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    Lexington, MA (USA)
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    Hello, eddieg0304!

    During a 9 hour snowstorm, it snows at a rate of 1 inch per hour for the first 2 hours,
    at 2 inches per hour for the next 6 hours, and at a rate of 0.5 per hour for the final hour.

    Write and graph a piecewise-defined function that gives the depth of the snow during the snowstorm.
    How many inches of snow accumulated from the storm?
    I sketched the graph first . . .
    Code:
            |
            |               R
         14+               o
            |         Q  *  :
         14 +         o     :
            |        *:     :
            |       * :     :
            |      *  :     :
            |     *   :     :
            |  P *    :     :
          2 +   o     :     :
            | * :     :     :
        - - o - + - - + - - + - -
            |   2     8     9
            |

    First 2 hours: 1 inch per hour.
    . . Point P\!:\;(2,2)

    Next 6 hours: 2 inches per hour.
    . . From t=2 to t=8, 12 inches of snow were added.
    . . Pont Q\!:\;(8,14)

    Last hour: inch per hour.
    . . From t = 8 to t = 9,\;\tfrac{1}{2} inch was added.
    . . Point R\!:\;(9,14.5)


    f(x) \;=\;\begin{Bmatrix}x && 0 \leq x < 2 \\ \\[-3mm]2x+2 && 2 \leq x < 8 \\ \\[-3mm] \frac{1}{2}x + 14 && 8 \leq x \leq 9 \end{Bmatrix}

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  3. #3
    Newbie
    Joined
    Mar 2010
    Posts
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    ok now i have a few questions.




    f(x) \;=\;\begin{Bmatrix}x && 0 \leq x < 2 \\ <br />
\\[-3mm]2x+2 && 2 \leq x < 8 \\ \\[-3mm] \frac{1}{2}x + 14 <br />
&& 8 \leq x \leq 9 \end{Bmatrix}<br />
    This function is it supposed to be that of the graph? cause if so would you be able to explain how so? i was just doing some checking on it and it didn't seem to pan out, but i am not a 100% sure as my calculator is sort of out of commission right now so i just did it all in my head since they are fairly simple equations, and most definitely thank you for even checking this out and giving me a helping hand
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