## Least Squares Fitting--Exponential

To fit a functional form

 (1)

take the Logarithm of both sides
 (2)

The best-fit values are then
 (3) (4)

where and .

This fit gives greater weights to small values so, in order to weight the points equally, it is often better to minimize the function

 (5)

Applying Least Squares Fitting gives
 (6)

 (7)

 (8)

Solving for and ,
 (9) (10)

In the plot above, the short-dashed curve is the fit computed from (3) and (4) and the long-dashed curve is the fit computed from (9) and (10).

See also Least Squares Fitting, Least Squares Fitting--Logarithmic, Least Squares Fitting--Power Law