1 Ingredients of Change: Functions and Linear Models

 Project 1.1: Tuition Fees Setting Nearly all students pursuing a college degree are classified as either part-time or full-time. Many colleges and universities charge tuition for part-time students according to the number of credit hours they are taking. They charge full-time students a set tuition regardless of the number of credits they take, except possibly in an overload situation. Tasks Find the tuition charges at your college or university. Some schools have different tuition rates for different classifications of students (for instance, residents may be charged a different tuition than nonresidents). Pick one classification to model. Write a piecewise linear model for tuition as a function of the number of credit hours a student takes. Consider charges such as matriculation and activity fees that all students must pay as being part of the college tuition. Use your model to generate a table of tuition charges for your school. Compare your table with the published tuition charges. Are there any discrepancies? If so, explain why they might have occurred. Even though you would not pay tuition if you registered for 0 credit hours, your model may have an interpretation at this point. What is that interpretation? Reporting Write a letter addressed to the Committee on Tuition. You should explicitly define to whom the model applies and what the variables in the model represent. Include an explanation of how to use the model, a statement about which input values are valid and which are invalid for use in the model, and a discussion of the preceding tasks.
 Project 1.2: Finding Data Setting Newspapers, journals, and government documents are good sources of data. Tasks Find (in a newspaper, journal, or government document) a set of data with more than 7 data points that would be reasonably modeled by a linear function. Fit a linear model to the data. What do your model's slope and intercept mean in the context of the data? Reporting Write a report in which you describe the meaning of the data, discuss the linear model you used to fit the data, and answer the question posed in Task 3. In your report, you should explicitly state the model, define the variables in the model, and state what input values are valid for this model. You should also include a scatter plot and graph of your model. Properly cite the source of your data using correct bibliographic form. Attach a photocopy of the data and the page on which the title of the article or document appears. Prepare a 3-5-minute oral presentation of your report. You should incorporate the use of visual aids to enhance your oral presentation.