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Thread: Rational Functions Word Problem

  1. #1
    Sep 2012

    Rational Functions Word Problem

    Experiments conducted by A.J. Clark suggest that the response R(x) of a frog's heart muscle to the injection of x units of acetylcholine (as a percent of the maximum possible effect of the drug) may be appromixated by the rational function
    R(x)=100x/b+x (x greater than or equal to 0)
    where b is a positive constant that depends on the particular frog.
    a. If concentration of 40 units of acetylcholine produces a response of 50% for a certain frog, find the "response function" for this frog.
    b. Using the model found in part (a), find the response of the frog's heart when 60 units of acetylcholine are administered.

    I am so confused by this problem.

    Help would be greatly appreciated.
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  2. #2
    Member kalyanram's Avatar
    Jun 2008
    Uppsala, Sweden

    Re: Rational Functions Word Problem

    Given $\displaystyle R(x)=\frac{100x}{b+x}$; where $\displaystyle R(x)$ is the response function (measure in percentage); $\displaystyle x$ (in concentration)
    a. Given $\displaystyle R(40)=50$ we need to now determine $\displaystyle b$ which is specific to the frog under test.
    $\displaystyle 50=\frac{100.40}{b+40} \implies b=40; \therefore R(x)=\frac{100x}{40+x}$
    Now you can try part (b).
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