Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Need help on setting up an equation of population

  1. Sep 29, 2010 #1
    1. So for my computer science course I was given the homework on how to write a program on population growth. The serious dilemma is how to set up the equation. Here are the variables that are given to me:

    J = original number of Jackalopes (the imaginary animal that my teacher used)
    Y = generation (no specific unit of time)
    P = new population after each generation
    b = born percentage each generation (3% or 0.03)
    d = death percentage each generation (1% or 0.01)

    Example: J = 40 Jackalopes
    Y = 100 generations
    P = new population of 291 Jackalopes after 100 generations




    2. The most relevant equation is population growth, which involves exponential functions. the equation looks like

    X = X0ert
    where:
    X0 is the original population
    r is the net rate of growth
    t is time

    The big problem is I can't use exponential functions, because I need to truncate the results and using exponential functions don't give the answer that my teacher is looking for.

    3. Here is the attempted solution I came up with:

    P = J + (J(0.03-0.01))Y

    unfortunately my answer is way off. I recognize the pattern when I attempted to do the equation, but I don't know how to set it up. Please help me!
     
  2. jcsd
  3. Sep 29, 2010 #2

    fzero

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    After one generation,

    P(1) = J + (b-d)J = (1+(b-d)) J

    After Y generations,

    P(Y) = (1 +(b-d))Y J.

    It's possible to derive an exponential law if we treat a continuous growth, but this formula is fine for discrete growth. If find P(100)=290, the discrepancy might be due to round off error in a computer code.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook