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Math Help - Differential equation

  1. #1
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    Differential equation

    Hi, I need some help on this DEQ

    A spherical raindrop evaporates at a rate proportional to its surface area. Write a differential equation for the volume of the raindrop as a function of time.

    The back of the book says the answer: dV/dt = -kV^(2/3) for some k > 0. Though I have no idea how.

    Thanks
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by RB06 View Post
    Hi, I need some help on this DEQ

    A spherical raindrop evaporates at a rate proportional to its surface area. Write a differential equation for the volume of the raindrop as a function of time.

    The back of the book says the answer: dV/dt = -kV^(2/3) for some k > 0. Though I have no idea how.

    Thanks
    Surface area of sphere:

    A= 4 \pi r^2

    Volume of sphere:

    V = \frac{4}{3} \pi r^3

    Now you are told that:

    \frac{dV}{dt} = c A

    for some constant c, but A \propto V^{2/3}, so:

    \frac{dV}{dt} = k V^{2/3}

    for some constant k

    RonL
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