Results 1 to 8 of 8

Math Help - Doubling Time from population growth equation

  1. #1
    Newbie
    Joined
    Sep 2007
    Posts
    5

    Doubling Time from population growth equation

    I need to isolate the variable n (years) from this equation:

    Pt = Po * (1 + {GR/100})^n

    I tried using logs:

    log Pt = log Po * n log (1 + {GR/100})

    then I tried n = _________log Pt_________
    log Po * log (1 + {GR/100})

    Dows anyone know where I am going wrong? Its been ages since i've used logs.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Apr 2005
    Posts
    1,631
    Your solution looks good to me. If the expressions were to be posted aligned, it could be better.

    You meant
    n = Log[Pt] / {Log[Po] *Log[1 +(GR /100)]}
    right?

    You're still good after all those ages.
    Because the Log[1 +(GR/100)] cannot be touched anymore.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Sep 2007
    Posts
    5
    awesome! but can it be furthur simplified, or is that the end of the equation... at least its usable.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Apr 2005
    Posts
    1,631
    I cannot simplify it any further.

    Log(a) *Log(b) is just that.
    It cannot be Log(a*b), no.
    Nor Log(a +b), no.

    Log(a +b) is just that also.
    It cannot be Log(a) +Log(b), no.
    Nor Log(a) *Log(b), no.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Sep 2007
    Posts
    5
    Is this right, then?



    Thanks for all your help!
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Joined
    Apr 2005
    Posts
    1,631
    Quote Originally Posted by conor View Post
    Is this right, then?



    Thanks for all your help!
    Whoa.

    Now that I've seen it like that, I'm sorry to mislead you.

    No, that is wrong a little bit.

    It should be like this:

    Pt = Po*[1 +(GR/100)]^n

    Log(Pt) = Log(Po) +n*Log[1 +(GR/100)]
    Log(Pt) -Log(Po) = n*Log[1 +(GR/100)]
    Log[(Pt) /(Po)] = n* Log[1 +(GR/100)]

    n = Log[Pt / Po] / Log[1 +(GR/100)] ---------------answer.

    --------------------------------------------

    Again, sorry. I was fresh from sleeping when I commented before.
    Last edited by ticbol; September 29th 2007 at 04:11 PM.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Sep 2007
    Posts
    5
    ohhhh because a = b*c
    then log[a] = log[b] + log[c]

    is that right?
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Newbie
    Joined
    Sep 2007
    Posts
    5


    TADAA!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. doubling time
    Posted in the Calculus Forum
    Replies: 3
    Last Post: August 16th 2009, 09:20 AM
  2. [SOLVED] population growth differential equation problem
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: February 10th 2009, 06:24 AM
  3. doubling time
    Posted in the Algebra Forum
    Replies: 1
    Last Post: January 26th 2009, 11:46 PM
  4. Doubling time!
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: January 23rd 2008, 09:50 PM
  5. exp growth/doubling period
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 29th 2007, 04:24 PM

Search Tags


/mathhelpforum @mathhelpforum