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Math Help - Related rates, Differential equations calculus.

  1. #1
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    Related rates, Differential equations calculus.

    Please help.
    Once a spherical shaped soufflé is put in the oven, its volume increases at a rate proportional to its radius.
    1. Show that the radius r cm of the soufflé, at t minutes after it has been put in the oven, satifies the differential equation dr/dt = k/r , where k is a constant.

    2. Given that the radius of the soufflé is 8 cm when it goes in the oven, and 12 cm when it´s cooked 3 minutes later, find, to the nearest cm, its radius after 15 minutes in the oven.
    Thanks!
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  2. #2
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    Grrr.... Scribbled it down and scanned it, hopefully you can read it.

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  3. #3
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    Thank you for your quick response, but I wasn´t able to open the file.
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  4. #4
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    Thanks
    1
    I am getting a slightly different answer.

    \frac{dr}{dt}=\frac{k}{r}

    Separate variables:

    rdr=kdt

    Integrate:

    \int{r}dr=\int{k}dt

    \frac{r^{2}}{2}=kt+c

    Using r(0)=8:

    32=k(0)+c

    c=32

    Using t(3)=12:

    72=k(3)+32

    k=\frac{40}{3}

    r=\sqrt{2(kt+32)}

    At t(15):

    r=\sqrt{2(\frac{40}{3}(15)+32)}=4\sqrt{29}\approx{  21.54}
    Last edited by galactus; May 21st 2008 at 11:50 AM.
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