Depending on which plot on the previous page you saw as “straight,” you should have concluded that the data could be modeled either by an exponential function, $y=a{b}^t$, or by a power function, $y=a{t}^b$. (In the exponential case, the same function may be described by $y=a{e}^{kt}$, where $b=e^k$.) In either case, to find an explicit function, you need to determine numerical values for the two parameters, \(a\) and \(b\). We repeat the Data Plot here, with additional inputs for your choice of parameters and model function. Note that you can view your model function, together with the data, in any of the three types of plot.

1. State clearly which type of function you think models the AIDS data, and why.

2. 

   In the graph that you saw as “straight,” the slope of the line tells you something about one of the two parameters. Estimate the slope, and determine a value for that parameter. (Remember that some or all of the actual coordinates in that linear plot are base-10 logs of data values.)

3. Now use one or more data points to estimate the other parameter. Choose your model function, and enter your selected values for \(a\) and \(b\) in the worksheet. View your function superimposed on the data points in both a Cartesian plot and one of the logarithmic plots. Adjust your values for \(a\) and \(b\) until you are satisfied with the model function.

4. Record your values for \(a\) and \(b\) for use in the next part. You will be using them again in another tool.

In the next part you will determine whether and how well your function models the data, and you will make any adjustments that are necessary to get a good fit.