## Topic Jâ€”Exponential Models and Model Comparison Techniques

### Objectives:

- Recognize when a dataset shows an exponential relationship between the variables.
- Use a spreadsheet to adjust the initial-value and slope parameters of an exponential formula so that the graph of corresponding points are close to the points graphed from a data set.
- Use the exponential formula that best fits the data as a model for the data, predicting the output
*y*value for any specified input*x*value. - Compare the extrapolation behavior of different types of model that fit the same data.
- Choose among linear, quadratic, and exponential models based on a graph of the dataset.
- Recognize the quality of a model based on whether positive and negative residual deviations are randomly distributed or grouped together.
- Modify a model formula to simplify the fitting process without changing the dataset.

### Overview: Additional tools for modeling

In an earlier topic, you learned how to find good model formulas for data whose pattern is a straight line or a parabola. In both cases, you used worksheets from Models.xls to find good parameters for the models. These worksheets were very similar, differing only in the formula placed in the C3 cell and in the names and meanings of the parameters in cell G3, G4, etc. Other models are just as easy.

In this topic we will add *exponential models*, useful when the output changes by the same percentage each step. We will also learn how to compare and choose among types of models. Finally, we will learn to modify the model formula when needed to make the graph or parameters more convenient.