# Doctors and Nurses

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

### Abstract 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.

• Content Area – Calculus, Nonlinear Functions, Modeling
• Time Frame – 4 to 5 weeks with mini lectures
• Published – January 18, 2011
• Keywords – rational functions, limits, modeling

### Project Content

Project Letter (DOC | PDF)
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.

How to Make a Scatter Plot in Excel (includes Regression too!) (Video)
Graphing a Function in Excel (Video)