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College Algebra

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The concentration C of a certain drug in a patient's bloodstream t minutes after injection is given by
C(t)=50t/t^2+25. Determine the time at which the concentration is highest. Round your answer to the nearest tenth of a minute.

  • College Algebra -

    C=50t/(t^2+25)

    It is a shame you are not in calculus, this is a trivial problem in calculus.


    In algebra, this will lead to a quatric equation, not an easy situation. Are you allowed to graph it?

    get your calculator, and graph
    y=50t/(t^2+25)

    I see a max at about 4.8 on this very inaccurate plotter.
    http://my.hrw.com/math06_07/nsmedia/tools/Graph_Calculator/graphCalc.html

  • College Algebra -

    I thought that could be the solution. I graphed it on my calculator and I come up with a maximum of 5. Does this seem correct?

  • College Algebra -

    I assume you meant

    C(t)=50t/(t^2+25)

    Since C(0) = C(∞) = 0, and C(t)>0 for t>0 we know there's a max in there somewhere.

    Can't think of any easy algebraic way to find the max, except some trial and error.

    C(4) = 4.87
    C(5) = 5.00
    C(6) = 4.91

    5 looks like a good candidate.

    C(4.9) = 4.999
    C(5.1) = 4.999

    Looks like t=5.0 is our guy.

  • College Algebra -

    Thank you. I looked at the table and 5 was 5 so I thought I was on the right track but just wanted to make sure. Thank you so much!

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