Results 1 to 2 of 2

Thread: Social Diffusion (Integration)

  1. #1
    Junior Member
    Aug 2012

    Social Diffusion (Integration)

    In a sufficiently large population the number x who have the information is treated as a differentiable function of time t The rate of diffusion, dx/dt, is assumed to be proportional to the number of people who have the information times the number of people who don't. This leads to the differential equation dx/dt = Kx(N-x), where N is the number of people in the population.

    Suppose t is measured in days, K=1/25, and 4 people start a rumor a time t=0 in a population N=100 people.

    a) Find x as a function of t by integrating both sides of the equation (1/(x(N-x))) dx = K dt
    b) When will half the population have heard the rumor?
    c) When will the rumor be spreading the fastest?

    I'm stuck and don't know where to go.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Sep 2012
    Washington DC USA

    Re: Social Diffusion (Integration)

    Quote Originally Posted by Preston019 View Post
    I'm stuck and don't know where to go.
    Do you need help translating the word problem? Or is it the integral you don't know how to do? Or is it all just a blur?

    Here's the set up, after translating the information in the word problem:

    $\displaystyle x(t)$ = number of people hearing the rumor at time t in days.

    $\displaystyle x(0) = 4$.

    $\displaystyle dx/dt = (1/25)(x)(100-x) = 4x - x^2/25$.

    a) FIND $\displaystyle x(t)$. Hint: $\displaystyle \int \frac{1}{x(100-x)} dx = \int (1/25) dt$.

    b) FIND $\displaystyle t_0$ such that $\displaystyle x(t_0) = 50$.

    c) FIND $\displaystyle t_1$ such that $\displaystyle \frac{dx}{dt}(t_1) = \max \{ \frac{dx}{dt}(t) | t \ge 0 \}$.
    Last edited by johnsomeone; Sep 18th 2012 at 11:56 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. nature of economics as social science?
    Posted in the Business Math Forum
    Replies: 7
    Last Post: Sep 18th 2011, 04:19 AM
  2. Replies: 9
    Last Post: Mar 27th 2010, 03:14 AM
  3. Social stats VERY IMPORTANT PLEASE!
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: Mar 3rd 2010, 12:20 PM
  4. Integration salt diffusion problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Aug 6th 2009, 02:26 AM
  5. Logistic Regression in Social Sciences
    Posted in the Advanced Statistics Forum
    Replies: 8
    Last Post: Jul 9th 2009, 04:35 AM

Search tags for this page

Search Tags

/mathhelpforum @mathhelpforum