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Math Help - if the radius of a sphere is increasing at a rate ...

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    if the radius of a sphere is increasing at a rate ...

    1) the radius of a sphere is increasing at a rate proportional to its radius. if the radius is 4 initially, and the radius is 10 after 2 seconds, what will the radius be after 3 seconds?

    2) use differentials to approximate the change in volume of a sphere when the radius is increased from 10 cm to 10.02 cm.
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    Quote Originally Posted by yoman360 View Post
    1) the radius of a sphere is increasing at a rate proportional to its radius. if the radius is 4 initially, and the radius is 10 after 2 seconds, what will the radius be after 3 seconds?
    \frac{dr}{dt}=kr

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

    \ln{r}=kt+C

    r(0)=4 so C=\ln{4}

    r(2)=10 so k=\frac{1}{2}\ln{\frac{5}{2}}

    r=4(2.5)^{\frac{t}{2}}

    Now find r(3)

    Quote Originally Posted by yoman360 View Post
    2) use differentials to approximate the change in volume of a sphere when the radius is increased from 10 cm to 10.02 cm.
    V=\frac{4}{3}\pi r^3

    dV=4\pi r^2\,dr

    r=10, dr=.02

    Find dV
    Last edited by ione; March 20th 2010 at 05:23 PM.
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