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Math Help - Concentration in brine solution

  1. #1
    Member jacs's Avatar
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    Concentration in brine solution

    A tank contains 100 litres of brine whose concentration is 3 grams/litres. Three litres of brine whose concentration is 2 grams/litre flow into the tank each minute and at the same time 3 litres of mixture flow out each minute.

    Show that the quantity of salt, Q gram, in the tank at any time t is given by:
    Q = 200 + 100e^(-0.03t)

    i have managed to get Q = 200 - 100e^(-0.03t)


    and cannot figure out why the minus is there, i have included the pdf of the working i have done so far, any help appreciated

    thanks
    jacs
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by jacs
    A tank contains 100 litres of brine whose concentration is 3 grams/litres. Three litres of brine whose concentration is 2 grams/litre flow into the tank each minute and at the same time 3 litres of mixture flow out each minute.

    Show that the quantity of salt, Q gram, in the tank at any time t is given by:
    Q = 200 + 100e^(-0.03t)

    i have managed to get Q = 200 - 100e^(-0.03t)


    and cannot figure out why the minus is there, i have included the pdf of the working i have done so far, any help appreciated

    thanks
    jacs

    In your solution you get to a line:

    t=-\frac{100}{3}\ln(600-3Q)+c.

    But now at t=0,\ Q=300 putting this into the above equation
    gives a term \ln(-300) not \ln(300) which you have.

    To avoid this change your integral to:

    t=-\frac{100}{3} \int \frac{3}{3Q-600}dQ,

    or:

    -0.03t=\ln(3Q-600)+C.

    Which if I have done this right should now allow you to get the
    given answer.

    RonL
    Last edited by ThePerfectHacker; January 16th 2006 at 02:46 PM.
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  3. #3
    Member jacs's Avatar
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    I see, thank you I had that originally, but since it yeilded the negative ln result, I assumed I had somehow messed it up.

    Of course, it is a simple matter to swap the sign to avoid that problem (now that you have pointed it out to me...lol.... )

    I bow before you genius

    thanks

    jacs
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