Results 1 to 3 of 3

Math Help - Differential Equations-Application of 1st order differential equations 1

  1. #1
    Junior Member
    Joined
    Sep 2008
    From
    Australia
    Posts
    72

    Differential Equations-Application of 1st order differential equations 1

    Sunlight transmitted into water loses intensity as it penetrates to greater depths. The rate at which the intensity decreases with depth is proportional to the intensity at that depth. At a depth of 10 metres, the intensity is 30% of its original intensity at the surface. At what depth would the intensity be 20% of that surface?

    What is the differential equation?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by sanikui View Post
    Sunlight transmitted into water loses intensity as it penetrates to greater depths. The rate at which the intensity decreases with depth is proportional to the intensity at that depth. At a depth of 10 metres, the intensity is 30% of its original intensity at the surface. At what depth would the intensity be 20% of that surface?

    What is the differential equation?
    Solve \frac{dI}{dx} = -kI subject to the boundary conditions I(0) = I_0 and I(10) = 0.3 I_0.

    Then solve I(x) = 0.2 I_0 for x.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Sep 2008
    From
    Australia
    Posts
    72
    OK...
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: May 7th 2011, 10:26 AM
  2. Application of 1st order differential equations 2
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: May 19th 2009, 03:52 AM
  3. Application of Differential Equations.
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: November 17th 2008, 09:54 PM
  4. Replies: 27
    Last Post: February 10th 2008, 05:49 PM
  5. Replies: 3
    Last Post: July 9th 2007, 05:30 PM

Search Tags


/mathhelpforum @mathhelpforum