National Numeracy Network > Teaching Resources > Quantitative Writing > Examples > Economic argument about increasing fuel efficiency

# Economic argument about increasing fuel efficiency

This material is replicated on a number of sites as part of the SERC Pedagogic Service Project

#### Summary

In the op-ed piece, Jerry Taylor argues that spending about \$1500 to modify pick-up trucks and SUVs to increase the fuel efficiency by 40-50% is unwise economically. In order to analyze and critique his arguments and conclusions, one must produce linear models of cost equations and exponential models of savings equations. In addition, one must make various assumptions to critique the conclusions because, as is often the case in such articles, the information is incomplete. The argument is purely economic, ignoring social and environmental issues involved.

## Learning Goals

• Modeling of linear and exponential growth
• Making reasonable assumptions
• Approximation and estimation
• Graphing linear and exponential functions
• Interpreting features of graphs in terms of the situation being modeled
• Comparing the results of models over time

## Context for Use

This activity can be done over a period of an hour in class or over several class periods depending on the extent to which the concepts of comparing linear and exponential growth are pursued. Students need to be familiar with college algebra graphing techniques and some basic economic facts. This can be done as a reasearch project where the students would need to find basic information such as the miles driven per year by the typical driver. The economic argument made depends only on the fuel costs of driving. Considering other costs – maintenance, insurance, depreciation, etc – would make the models much more complicated.

## Description and Teaching Materials

There are three documents here:
1. The text of the article that is the subject of this assignment.
Taylor, J (2001) Forcing fuel efficiency on consumers doesn't work (Microsoft Word 29kB May12 08), Lincoln (NE) Journal Star.
2. A brief introduction to the assignment and then the six items (some with several parts) that guide the assignment report.
Student version of case study of the article (Microsoft Word 38kB May12 08)
3. The instructor version of the assignment with a set of possible responses to the six items.
Instructor version of case study (Microsoft Word 206kB May12 08)

## Teaching Notes and Tips

One way to begin this assignment with students who have little experience in mathematical modeling is to ask the students to determine the fuel cost savings after five years and after ten years. They can also determine the value of the 5% savings account after five and ten years. This information should guide them to conjectures about the validity of the author's assertions.

The assignment can be extended in several directions and require several class periods for discussion and resolution. Alternatively, the assignment can be made for students to complete a written report outside of class.

Completing the entire assignment as presented, students will model situations with linear equations (savings equation or cost equation from fuel economies) and exponential equations (savings accounts). In addition, students will find installment savings totals (sum of a geometric series or using sum(seq( commands on a TI calculator). Preparing students for this with simpler and pre-packaged examples can shorten the time required to discuss the assignment in class.

## Assessment

The results that I value are the following:
1. Students made reasonable estimations about the validity of the three quantitative assertions that the author makes;
2. Students recognized what assumptions must be made to check the assertions;
3. Students made reasonable assumptions for miles driven per year and cost of a gallon of gasoline in 2001 when the article was written;
4. Students recognized what their models did not take into account (for example, most will assume a constant cost of gasoline over time and not take all costs of operating an automobile into account);
5. Students recognized that increased costs of gasoline and more miles driven per year will increase the savings in fuel costs by increasing efficiency;
6. Students recognized what certain features of the graphs (for examples, intercepts on the axes or points of intersection) meant in the context of savings; and
7. Students recognized that the author may have been making different assumptions to reach his conclusions and investigate what these assumptions might have been.

One way to assess parts of the learning goals of this assignment is to ask students to model the savings accruing from fuel cost reduction by purchasing a hybrid automobile. You can either specify gasoline costs and miles driven per year or you can require the students to make assumptions. Be sure to make conclusions written in complete sentences part of the assessment.