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Math Help - modelling functions

  1. #1
    Junior Member
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    Exclamation modelling functions

    A gas tank on a dock has a small puncture and is leaking gas at the rate of
    1cm^3/min into a lake. It forms a circular slick that is 1mm thick on the surface of the water.

    a) Find the amount of gas leaked as a function of time.

    b) State the radius of the slick as a function of its volume

    c) State the radius of the slick as a function of time.

    d) What is the radius of the slick after 40 minutes?
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  2. #2
    Senior Member Twig's Avatar
    Joined
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    Gothenburg
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    Hi

    You say nothing about how much gas had already leaked out. Or is this assumed to be zero ?

    You have that gas is leaking out with 1 cm^{3}/min , so lets say the time variable  t is in minutes.

    Call  y the amount of gas leaked out. Then:

    \frac{dy}{dt}=-1\cdot 10^{-6} m^{3}/min \; \Rightarrow y(t) = -t\cdot 10^{-6} + C \; m^{3} Set  C = 0 if none had already out.

    The gas forms a cylinder on the water.

     V = \pi r^{2} h \; This gives us:  r = \sqrt{\frac{1000V}{\pi}} , since we are using SI-units here, that is calling 1mm = 0.001m .

    To find the radius as a function of the amount of gas, interchange V for  y(t)
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