This prompt is open ended, and a large part of the goal is to provide some national financial literacy. Students look up the data for themselves, decide whether to use all of the data (that is, on an annual basis) or just a few data points (for example, every 5 years), and think carefully about which type of model to use. Choices include: 

• Linear
• Quadratic (if done later in the course)
• Exponential
• Piecewise

Students use statistical tools to produce different models and compare their residuals.

Because there are so many factors involved in the debt (changes to programs, such as Medicare and Social Security, changes to taxation, and natural disasters at home and abroad), there is no way to expect any reliability in a model over the long term. Moreover, growth in the debt needs to be compared to growth in overall wealth (33 trillion dollars isn’t as much of a problem when the overall wealth in the country is 150 trillion dollars). For students to more fully understand debt issues, prompt them to examine topics such as inflation, income distribution, and the national budget.

In this version of the prompt, students are instructed to look at the U.S. debt every other year, and two types of models are suggested (linear and exponential). The main work facing students in this version likely includes:

• Looking up data
• Choosing an exponent for an exponential model (especially if they do not use graphing technology to find a good match)
• Taking into account that the data is given for every other year, not every year, when writing an equation for their model.

As in the first version, share extra information, with students, to put the current debt into an appropriate historical perspective as they work on the problem.

In this version of the prompt, students are given the data and told to look at the debt every other year. They also are told that a linear model is not appropriate and asked to explain why. While students are not told that an exponential model is a good fit for the data, they are asked to find an exponential model that they think works well. Thus, the main lifting for students in this version is:

• Finding an appropriate exponential model by hand or with the aid of technology.
• Dealing with the fact that the data is given in two-year chunks, rather than every year, if they write the exponential model as a function.