Problem

After examining the data in the table, it is suggested that since the amount of damage is increasing so quickly, perhaps an exponential function would be a better fit. Is this true? Find the best-fit exponential function and determine if it does in fact model the data more precisely.

Solution

Using the applet on the course Web page for unit 1.07, enter the data from the previous example and click "Best Semi-log Exponential Fit". The result is the equation

However, the exponential fit error listed for us is about 56 million, which is significantly higher that the error for either of the polynomial functions in the previous example. Therefore we conclude that the exponential model is not a better fit.