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Math Help - serium

  1. #1
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    serium

    Dear Sir
    I would be grateful if you can help me to solve the the below questions
    I managed to get the answer to part (a) but cannot get the time 11.16 minutes in part b

    thanks
    Kingsman

    I
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by kingman View Post
    Dear Sir
    I would be grateful if you can help me to solve the the below questions
    I managed to get the answer to part (a) but cannot get the time 11.16 minutes in part b

    thanks
    Kingsman

    I
    This is a seperable differential equation with solution:

    x=10+Ae^{-t/50}

    As x(0)=20, we have A=10

    so:

    x=10(1+e^{-t/50})

    To find when x(t)=18 we solve:

    10+Ae^{-t/50}=18

    which has solution:

    t=-50 \ln(0.8)=11.16 minutes (rounded to two places of decimal)

    CB
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