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Math Help - the rate at which a purification process can remove contaminants from a tank of water

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    the rate at which a purification process can remove contaminants from a tank of water

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    Quote Originally Posted by yoman360 View Post
    Let A = the amount of contaminant in the water

    \frac{dA}{dt}=kA

    \frac{dA}{A}=k\,dt

    ln|A|=kt+C

    Let the amount of contaminant when t = 0 be 100

    ln100=C

    ln|A|=kt+ln100

    Since 20% of the contaminants can be removed during the first minute

    A=80 when t = 1

    ln80=k(1)+ln100

    k=ln\frac{4}{5}

    ln|A|=(ln\frac{4}{5})t+ln100

    You want to find t when A = 2
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