The Spread of AIDS

Part 2: Finding a Model Function

Depending on which plot in part 1 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.

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 logs of data values.)
3. Now use one or more data points to estimate the other parameter. Enter your model function in the worksheet.

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.