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Math Help - Exponential Functions!!

  1. #1
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    Exponential Functions!!

    The concentration C in part per million, of a medication in the body t hours after ingestion is give by the function

    C(t)= 10t^2e^-t

    1. Find the rate of change of the concentration
    I know this is the derivative, but the derivative the book give me is not like the one I got. I have

    C'(t)=20te^-t - 10t^2e^-t


    2. Find the maximum value of the concentration and where it occurs.
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  2. #2
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    Quote Originally Posted by littlesohi View Post
    The concentration C in part per million, of a medication in the body t hours after ingestion is give by the function

    C(t)= 10t^2e^-t

    1. Find the rate of change of the concentration
    I know this is the derivative, but the derivative the book give me is not like the one I got. I have

    C'(t)=20te^-t - 10t^2e^-t


    2. Find the maximum value of the concentration and where it occurs.


    C(t)=10t^2e^{-t}

    Apply the product rule:

    C'(t)=20te^{-t}-10t^2e^{-t}

    ----------------------------------------------------
    =10e^{-t}(10-t^2)
    ----------------------------------------------------
    EDIT: I factored that wrong. It should be:

    C'(t)=10te^{-t}(2-t)

    I have no idea how I managed that. It's a good thing pickslides pointed that out.

    So you were right about the derivative.
    Last edited by adkinsjr; November 8th 2009 at 04:34 PM.
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  3. #3
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    Quote Originally Posted by littlesohi View Post


    2. Find the maximum value of the concentration and where it occurs.
    Solve this

    C'(t)=0

    te^{-t}(20-10t)=0
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  4. #4
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    Is this correct?

    Quote Originally Posted by adkinsjr View Post

    C'(t)=20te^{-t}-10t^2e^{-t}

    =10e^{-t}(10-t^2)


    10e^{-t}(10-t^2) = 100e^{-t}-10t^2e^{-t} \neq 20te^{-t}-10t^2e^{-t}
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  5. #5
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    Quote Originally Posted by pickslides View Post
    Is this correct? NOPE!





    10e^{-t}(10-t^2) = 100e^{-t}-10t^2e^{-t} \neq 20te^{-t}-10t^2e^{-t}
    I edited the post. It seems I factored that wrong.
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