**Author **David Graser, Yavapai College, Prescott, AZ (David_Graser@yc.edu)

**Abstract**

These projects originated from the College Costs project. In that project, students modeled costs at educational institutions to determine when costs will double. This goal allowed me to use a unique dataset available from the College Board. This dataset of college costs across the US is updated each year. In these projects, students model costs in different states with different types of models. The goal is to use the functions to determine how much is saved in that state by attending a community college for two years and the a four-year college for another two years versus attending a four-year college for all four years.

All of these projects use Excel to make the scatter plots and corresponding models.

- Content Area – College Algebra
- Time Frame – 4 Weeks with Mini Lectures for each project
- Published – March 21, 2012
- Keywords – point-slope form, line, slope, data, linear, rate, quadratic, exponential, logarithmic

**Project Content**

**Project Letter (Linear):** DOC | PDF

**Project Letter (Quadratic):** DOC | PDF

**Project Letter (Exponential):** DOC | PDF

**Project Letter (Logarithmic):** DOC | PDF

**Scaffolding Resources**

**Technology Assignment – Make a Scatter Plot of College Costs** ( DOC| PDF): This assignment is designed to get the students graphing their data points in Excel.

**Technology Assignment – Find a Linear Function for College Costs** ( DOC| PDF): In this assignment, students find linear functions for the two datasets they were assigned. They add the lines to the scatter plots created in the technology assignment above.

**Technology Assignment – Paste Equations and Graphs** ( DOC | PDF ): In this assignment, students paste the graphs they have created as well as corresponding equations into a Word document.

**Technology Assignment – Use Matrices to Find a Model** (DOC | PDF): In this assignment, students find the linear model using matrices. This is a lead in for the quadratic project.

**Technology Assignment – Find a Quadratic Function for College Costs** (DOC | PDF): Students apply the matrix technique illustrated above to find a quadratic function that passes through three of the data points in the college cost data.

**Technology Assignment – Find an Exponential Function for College Costs** (DOC| PDF): Students find an exponential model for college costs of the form *y* = *P* *e ^{rt}*.

**Notes**

- Make sure students understand the two options that they are to compare. Many of my community college student don’t even imagine completing a four-year degree so the basic task is a bit mystifying to them.
- I emphasize using exact values for slope so many of the models will have fractions for the slope and y-intercept. A discussion of why this is important is useful.
- Since students develop a linear function for two-year colleges and a linear function for four-year colleges, this is a great place to utilize function notation. Good function notation makes it easy to explain how to find the total cost of the four years of education.
- Earlier versions of the Technology Assignments include instructions for using Mathtype as well as the equation editor in Word. Since most students use versions of Word that include the equation editor, I have deleted instructions for using Mathtype.