Results 1 to 2 of 2

Math Help - logistics and integral calculas

  1. #1
    Newbie
    Joined
    Oct 2007
    Posts
    9

    Post logistics and integral calculas

    Can somebody please help me with this homework question. I haven’t got much of an idea on what to do!

    Infection rate of a disease has a constant of 0.004, this may be represented mathematically by -

    dN/dt = 0.0004N(1000-N), N(0)=1

    1. Using Integral calculus derive a model to determine the number of people with this disease and any time “t”.

    2. Use this model to predict how long it will take for 75% of the population will be infected. Population = 1000

    3. Discuss the limitations of the model for long term predictions.



    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor kalagota's Avatar
    Joined
    Oct 2007
    From
    Taguig City, Philippines
    Posts
    1,026
    Quote Originally Posted by softdrink_jr View Post
    Can somebody please help me with this homework question. I haven’t got much of an idea on what to do!

    Infection rate of a disease has a constant of 0.004, this may be represented mathematically by -

    dN/dt = 0.0004N(1000-N), N(0)=1

    1. Using Integral calculus derive a model to determine the number of people with this disease and any time “t”.

    2. Use this model to predict how long it will take for 75% of the population will be infected. Population = 1000

    3. Discuss the limitations of the model for long term predictions.
    \frac{dN}{dt} = 0.0004N(1000-N)
    \implies \frac{dN}{0.0004N(1000-N)} = dt
    taking the integral of both sides:
    \int \frac{dN}{0.0004N(1000-N)} = \int \left( {\frac{0.001}{0.0004N} + \frac{2.5}{1000-N}} \right)dN = t + c
    if my partial fraction is correct, then you can continue from here..
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Logistics Regression: Odds Ratio for model with interactions
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: August 9th 2010, 02:54 AM
  2. Logistics formula
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: December 6th 2009, 07:06 PM
  3. Replies: 0
    Last Post: November 29th 2009, 10:10 AM
  4. Logistics Model
    Posted in the Calculus Forum
    Replies: 5
    Last Post: January 20th 2009, 10:30 PM
  5. integral calculas???
    Posted in the Calculus Forum
    Replies: 3
    Last Post: November 1st 2007, 05:10 AM

Search Tags


/mathhelpforum @mathhelpforum