Results 1 to 2 of 2

Math Help - Tub Leaking Problem

  1. #1
    Newbie
    Joined
    Feb 2011
    Posts
    6

    Tub Leaking Problem

    This is a question from my ODE class so I assume it's ok to post here

    the problem is
    A 200 gallon tank, initially full of water, develops a leak at the bottom. Given that 20% of the water leaks out in the first 4 minutes, find the amount of water left in the tank t minutes
    after the leak develops if:
    (i) The water drains off a rate proportional to the amount of water present.
    (ii) The water drains off a rate proportional to the product of the time elapsed and the
    amount of water present.
    (iii) The water drains off a rate proportional to the square root of the amount of water
    present.

    I really only need help with the first one so I can get an idea of what I'm supposed to do.
    I went through the whole hoopla of integrating etc. etc. and got this:

    V(t) = 200e^{ln(.8)t/4}

    However, the solution to the problem given in the back of the book is like so:

    V(t) = 200(4/5)^{t/4}

    Edit: super stupid moment
    I forgot that e^{ln(.8)}=4/5
    epic facepalm
    Follow Math Help Forum on Facebook and Google+

  2. #2
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    What DE did you use to model (i)?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Word problem involving the weather and a leaking barrel
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: November 10th 2010, 07:17 PM
  2. rate of growth of a leaking oil tank
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: March 30th 2009, 10:47 AM
  3. Work: Leaking flour
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 5th 2007, 06:56 AM

Search Tags


/mathhelpforum @mathhelpforum