Results 1 to 7 of 7

Math Help - I know you're gonna dig this Maths enthusiasts (challenging)

  1. #1
    Newbie
    Joined
    Aug 2012
    From
    London
    Posts
    15

    I know you're gonna dig this Maths enthusiasts (challenging)

    Birth rates of animal populations are typically not constant but vary periodically with the passing seasons. Find an expression for P(t) if the population dynamics are governed by the differential equation:

    dP/dt=(k+bcos2(pi)t)P

    Where 't' is in years and k>0. Compare the growths of a population where b>0 with one where b=0 at the end of a full year. Both populations have the same initial value Po
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,693
    Thanks
    1466

    Re: I know you're gonna dig this Maths enthusiasts (challenging)

    Pretty straight forward separable equations.

    With b> 0 you have \frac{dP}{P}= (k+ b cos(2\pi t) dt and with b= 0, \frac{dP}{P}= k dt.

    Those are easy to integrate.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Dec 2010
    Posts
    61

    Re: I know you're gonna dig this Maths enthusiasts (challenging)

    Quote Originally Posted by HallsofIvy View Post
    Pretty straight forward separable equations.

    With b> 0 you have \frac{dP}{P}= (k+ b cos(2\pi t) dt and with b= 0, \frac{dP}{P}= k dt.

    Those are easy to integrate.
    What is the answer after integration?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,553
    Thanks
    1419

    Re: I know you're gonna dig this Maths enthusiasts (challenging)

    Quote Originally Posted by NFS1 View Post
    What is the answer after integration?
    You can't integrate \displaystyle \begin{align*} \int{\frac{1}{P}\,dP}  \end{align*} and \displaystyle \begin{align*} \int{k\,dt} \end{align*}?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,693
    Thanks
    1466

    Re: I know you're gonna dig this Maths enthusiasts (challenging)

    Well, that's for KayAB to answer! They are pretty straight forward integrations. And since KayAB is asking about differential equations, I assume s/he can do integration.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Junior Member
    Joined
    Dec 2010
    Posts
    61

    Re: I know you're gonna dig this Maths enthusiasts (challenging)

    Quote Originally Posted by HallsofIvy View Post
    Well, that's for KayAB to answer! They are pretty straight forward integrations. And since KayAB is asking about differential equations, I assume s/he can do integration.
    KayAB has gone AWOL so can u solve the mystery?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,934
    Thanks
    336
    Awards
    1

    Re: I know you're gonna dig this Maths enthusiasts (challenging)

    Quote Originally Posted by NFS1 View Post
    KayAB has gone AWOL so can u solve the mystery?
    Let's start with the easy one.
    \displaystyle \begin{align*} \int{k\,dt} \end{align*}

    k is a constant, so \displaystyle \begin{align*} \int{k\,dt} \end{align*} = \displaystyle \begin{align*} k \int{,dt} \end{align*}

    How do you do this integration?

    -Dan
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. O Level maths needs Degree maths Knowledge
    Posted in the New Users Forum
    Replies: 5
    Last Post: May 20th 2012, 07:15 AM
  2. Should I buy maths books to teach myself maths.
    Posted in the Math Topics Forum
    Replies: 2
    Last Post: November 21st 2011, 03:45 PM
  3. Replies: 4
    Last Post: March 16th 2009, 10:52 AM
  4. Me again, dunno wot I am gonna do wif maths! lol
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: April 21st 2008, 12:57 PM
  5. Replies: 0
    Last Post: September 5th 2007, 02:50 AM

Search Tags


/mathhelpforum @mathhelpforum