Math

I really need help to find the answer to this question below. If possible, please show every step of the way in a detailed form so i can understand, it takes me a while to fully comprehend whats being done. Thank you so much.

QUESTION: the data shown model the growth of a rabbit population in an environment where the rabbits have no natural predators. Determine an algebraic model for the data.

Year: Rabbit Population:
1955 650
1958 2180
1960 5300
1961 8200
1962 12400
1965 35000
1968 66300
1975 91600
1980 92900
1986 92800
1990 93100

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asked by Yoyo
  1. I think this is an example of logistic growth, since the population will rise sharply until the food supply gives out, limiting further growth.

    I'm not really up on curve fitting for logistic growth, but the general curve is

    y = 1/(1+(1/a-1)e^(-rt))

    where a is y(0)/y(∞)
    In this case, y(0) = 650 and y(∞) looks to be about 93200

    So, I used the function

    93200/(1+(1/.00697-1)e^(-.3x))

    over the 35 year span shown above. The graph is at

    http://www.wolframalpha.com/input/?i=93200%2F%281%2B%281%2F.00697-1%29e^%28-.3x%29%29+for+0%3C%3Dx%3C%3D35


    Generating a table, the data do not seem to match yours very well, but maybe you can tweak things a bit.

    http://www.wolframalpha.com/input/?i=table+93200%2F%281%2B%281%2F.00697-1%29e^%28-.3x%29%29+for+x%3D0..35

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    posted by Steve

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