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Math Help - ?Quadratic inequality problem

  1. #1
    Newbie
    Joined
    Mar 2008
    Posts
    15

    ?Quadratic inequality problem

    Here goes -
    The percent W of municipal solid waste recovered is shown in the bar graph. The linear model is W=.737x + 25.7, where x = 0 represents 1995, x=1 represents 1996 and so on.
    Based on this model, when did the percent of waste recovered first exceed 26%?
    In what years was it between 26% and 28%?
    Well looking at the table anybody can reach the answer, but I can not lay it out in a formula that makes sense.
    I was trying to do 26.4> .737x + 25.7
    which comes to .949 > x, what would you do with that?
    How should this problem be setup?

    The bar graph looks like this
    year percent
    1995 26.0
    1996 26.4
    1997 27.2
    1998 27.4
    1999 28.1
    2000 30.1
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  2. #2
    Junior Member teuthid's Avatar
    Joined
    Feb 2008
    From
    Bowling Green, OH
    Posts
    49
    if the bar graph were absent, and I only had the model to work with, here are the setups that I would use:

    26<.737x+25.7

    26<.737x+25.7<28

    The trick to this problem is interpreting the results. the domain of this model is {0,1,2,3,4,5}, but the solutions to the inequalities are unlikely to be one of these six integers. Solving the first inequality you find that x>.408. To answer the question choose the domain element(s) that satisfies this inequality. Since 1>.408, we say that the waste recovered first exceeded 26% in 1996.

    p.s. the word "quadratic" implies that were dealing with x^2 terms. What you have here is a linear inequality.
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