AiS Challenge 2003 STI :: Kangaroos

  1. Real Problem: One of our aunts who lives on the Murray River in Victoria, Australia, has a deal for us. She would like to invest in a Down Under Theme Park in New Mexico. She would like us to go in with her on this. All we have to do is provide the labor — she'll provide the money. Should we accept this offer?

    The aunt will send us 25 pairs of kangaroos.
    She is in for ten years.
    She will give us start up money of $1M Aus.

    Some questions to explore: How fast will the herd grow? Are the conditions right for 'roos? How much land will will be needed? Where will the Park be located and why? What is the profit margin here?

  2. Working Problem: Let's start with one part of the problem: the growth of the herd. Assume this is a closed system (i.e. no predators or other environmental factors). Male/Female pairs have 1 offspring/year (i.e. an annual growth rate of 1/2). The average lifespan of a kangaroo in captivity is 3 years (i.e. an annual death rate of 1/3).

  3. Math Model: Let x(t) be the number of 'roos at time t. Then in an time interval dt, x(t) increases by 1/2*x(t). In addition, x(t) increases negatively (decreases) in dt by the amount 1/3*x(t). So, the net population increase of x(t) in the time interval dt is
    x(t + dt) = x(t) + 1/2*x(t) - 1/3*x(t)
    which reduces to the following:
    x(t + dt) = 1/6*x(t)

  4. Computational Model: There are many ways to implement a model for population growth interactions on a computer; e.g., Java, C++, or Excel. A "for loop" or similar construct will be useful.
    Sample Java Program

  5. Results/Conclusions: Plot a time history of the 'roo population. Comment on your results. Can you think of ways to refine your model?
    Sample Data (Output from the Java Program)

    Sample Graph (Gnuplot graph of our Data)