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Thread: function model2

  1. #1
    Senior Member
    Oct 2008

    function model2

    it is a beautiful day at the fair. the u.v. index for the day is 8, or high, so sunscreen is a must for young folk. the effectiveness is indicated by the sunscreen protection factor (SPF). the higher the SPF number the fewer u.v. rays can penetrate to burn the skin. when the protection factor (SPF), s, is known you can determine the percent,p, of the suns u.v. rays that pass through it by using the following model

    $\displaystyle p=\frac{100}{s}$

    a/ what are the asymptotes of the function? someone determined both horizontal and vertical were 0, but what does that mean in the context of this problem?
    b/ how would i graph this?
    c/ figure out the percent when SPF=35 so 100/35=2.8%..?
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  2. #2
    Super Member
    Jul 2009
    This is a function in the "general" form of $\displaystyle 1/x$. The graph of $\displaystyle 1/x$ takes on all values except for $\displaystyle x=0$, and thus 0 is indeed a vertical asymptote of the function. This makes sense for you as you know that you can not divide a number by 0. However what about the horizontal asymptote? Try to solve for $\displaystyle 0=1/x$, and see what you get.

    Now lets take a look at negative values of x (or s in your problem). With negative values of s, we get a "negative" percentage. However, does that make sense in the CONTEXT of this problem.

    I'll give you another example involving context. Lets say the amount of miles I can drive a car is modeled by the function: $\displaystyle M=30X$, where X is the amount of fuel in my car. The graph of $\displaystyle M=30X$ is a straight line that takes on ALL real numbers. However lets think about this in the CONTEXT of the problem. Can I put in NEGATIVE values for X? Of course not, I can't drive on negative 10 gallons of gas can I?

    The same applies to your problem above. Break down the problem and try to make a sentence out of what the equation is. For my problem it would be:

    If I put in negative gallons of fuel, I will drive negative miles!
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