PBL Pathways

Content Area

Calculus, Nonlinear Functions, Modeling

Time Frame

4 to 5 weeks with Mini Lectures


January 18, 2011


Rational functions, limits, modeling

Project Title

Doctors and Nurses


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


This project is designed to use the same strategy as Students and Teachers 2. Students model the data for the number of nurses and teachers as a function of time with a polynomial function and then combine these models into a rational function. Once this model is formed and gives reasonable behavior, they locate when the ratio model gives a specific output and the location of any horizontal asymptotes.

Project Content

Project Letter: DOC | PDF (Updated 2/17/11)
Project Data: Excel | PDF

Scaffolding Resources

Technology Assignment : Scatter Plot DOC | PDF - In this tech assignment, students learn how to make a scatter plot in Excel.

Technology Assignment: Regression Model  DOC | PDF - In this tech assignment, students use the scatter plot above and find linear model of the number of nurses and doctors as a function of time.

Technology Assignment: Rational Model DOC | PDF - To account for the asymptotic behavior that some datasets display, students model the number of students and teachers separately in the previous technology assignment. In this assignment, the functions are combined to create a rational function to model the nurse to doctor ratio. Students are given the option of using Mathtype or the equation editor in Word to create the formula of the rational function.

Technology Assignment: Limits at Infinity DOC | PDF - This tech assignment helps students to compute the asymptotic behavior of the rational function they have produced.

Video: How to Make a Scatter Plot in Excel (includes Regression too!)
Video: Graphing a Function in Excel
Video: Adding Axes Titles To Your Excel Graph
Video: Adding a Chart Title to your Graph
Video: Changing a Graph in Excel
Video: Graphing a Function on a TI-83 (or TI-84)
Video: How to Make a Scatter Plot on a TI-83 (or TI-84) includes Linear Regression too!
Video: Quadratic Regression on the TI-83 (or TI-84)
Video: Documenting Your Solution to an Equation Using Mathtype
Video: Documenting the Limit of a Rational Function in Mathtype
Video: Use Your TI-83 (or TI-84) to Generate a Table for a Limit



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