Exponential regression can be done on a calculator, if the calculator has the correct package. But we can "massage" the data a little to get it into a form where we can do a linear regression to get the coefficients a and b.
Given the equation , take the natural logartithm of both sides:
This is now in the form: (a line) where , , and
So do the following to your data set: (I am setting the year '83 - '84 to be x = 1)
Do a linear regression on this data. You'll get values M for the slope and B for the intercept.
Then your value for a will be and your value for b will be .
(I got a = 90.93000 and b = -0.17638 using the model . The correlation coefficient was 0.96 or so, indicating a good fit.)