Results 1 to 3 of 3

Math Help - population growth with differential

  1. #1
    Newbie
    Joined
    Apr 2009
    Posts
    16

    population growth with differential

    Population y grows according to the equation dy/dt=ky where k is a constant and t is measured in years. if the population doubles every 10 years then the value of k is?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member redsoxfan325's Avatar
    Joined
    Feb 2009
    From
    Swampscott, MA
    Posts
    943
    Quote Originally Posted by lbj2322 View Post
    Population y grows according to the equation dy/dt=ky where k is a constant and t is measured in years. if the population doubles every 10 years then the value of k is?
    Separate and integrate:

    \int\frac{dy}{y} = \int k\,dt \implies \ln(y)=kt+C \implies y=c_0e^{kt}

    We are looking for the value of k that makes e^{10k}=2, so k=\frac{\ln 2}{10}\approx0.0693.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Apr 2009
    Posts
    16
    thanks again for the help

    when i did the differential i did come upon y=Ce^kt but i wasnt sure how to represent a population doubling every 10 years.
    now i understand
    thanks again
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. population growth differential eq.
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: October 4th 2009, 10:48 PM
  2. [SOLVED] population growth differential equation problem
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: February 10th 2009, 05:24 AM
  3. Population growth with non-constant growth factor
    Posted in the Differential Equations Forum
    Replies: 0
    Last Post: February 3rd 2009, 04:46 PM
  4. [HELP] Population Growth
    Posted in the Pre-Calculus Forum
    Replies: 8
    Last Post: October 27th 2008, 12:14 AM
  5. Population Growth
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: November 26th 2007, 04:38 AM

Search Tags


/mathhelpforum @mathhelpforum