Results 1 to 4 of 4

Math Help - Rate of change. Forming an equation

  1. #1
    Newbie
    Joined
    Apr 2010
    Posts
    15

    Rate of change. Forming an equation

    A forest is buring so that, t hours after the start of the fire, the area is A hectares. It is given that, at any instant, thhe rate at which the area is increasing is proportional to A^2.

    i) Write down a differential equation which models this situation.

    \frac{dt}{dA}= A^2 ?


    ii)After 1 hour, 1000 hetares have been burnt; after 2 hours, 2000 hectares have been burnt. Find after how many hours 3000 hectares have been burnt.

    Am i right for part i)?
    Not sure how to do part ii)
    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 George321 View Post
    A forest is buring so that, t hours after the start of the fire, the area is A hectares. It is given that, at any instant, thhe rate at which the area is increasing is proportional to A^2.

    i) Write down a differential equation which models this situation.

    \frac{dt}{dA}= A^2 ?


    ii)After 1 hour, 1000 hetares have been burnt; after 2 hours, 2000 hectares have been burnt. Find after how many hours 3000 hectares have been burnt.

    Am i right for part i)?
    Not sure how to do part ii)
    Read what the question says:

    It is given that, at any instant, thhe rate at which the area is increasing is proportional to A^2.
    So \frac{dA}{dt} \propto A^2 \Rightarrow \frac{dA}{dt} = k A^2 where k is a constant.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Apr 2010
    Posts
    15
    Why is there a K and how do you do part ii)?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by George321 View Post
    Why is there a K and how do you do part ii)?
    k is the proportionality constant. You're expected to be familiar with the topic 'Variation' - I suggest you review it.

    For part ii), the first step is to get the general solution to the DE. Show you working. Then I'll explain the second step.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. RATE OF CHANGE differential equation
    Posted in the Differential Equations Forum
    Replies: 11
    Last Post: August 8th 2011, 01:09 PM
  2. Replies: 3
    Last Post: April 12th 2011, 09:51 AM
  3. differential equation from related rate of change.
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: February 21st 2011, 01:37 AM
  4. Forming an equation
    Posted in the Algebra Forum
    Replies: 1
    Last Post: March 17th 2010, 05:17 PM
  5. writing equation for integration regarding rate of change
    Posted in the Differential Equations Forum
    Replies: 8
    Last Post: January 5th 2010, 04:24 AM

Search Tags


/mathhelpforum @mathhelpforum