How do I write an exponential model using a given table of values?

I have a table of values telling the Swan Population in Michigan for certain years. I've checked the first and second differences, neither of which are constant and I'm not sure where to go from there. Also, the years do not have a constant difference either.

The values are:

1987=4

1990=10

1991=45

1996=140

1999=285

2000=400

2003=565



I need to predict what the number will be in 2012.How do I write an exponential model using a given table of values?
When you suspect that your data may be exponential, a semilog plot is a powerful tool for evaluating the data. Plot ln(Y) versus X. If the data are exponential, the points on the plot will appear to be linear.



I made a semilog plot of your data and found that the points from 1991 to 2003 are fairly linear. The points for 1987 and 1990 appear to be from a different population, so I omitted them from the linear regression.



Excel's linear regression gave this model:



ln(Y) = -432.2264668 + 0.219027072X



where Y is the swan population and X is the year. Plugging in X = 2012 gives



ln(Y) = -432.2264668 + 0.219027072(2012)



= 8.456001291



Hence, Y = e^8.456001291 = 4703.213565



So the predicted vale for 2012 is 4703.