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

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

Steve · Answer

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