11.5 Choose the Best Model for Two-Variable Data

Example 1

Teacher’s Salaries The table shows the teacher’s salary y (in dollars) for a certain school district, where x is the number of years of teaching experience. Use a graphing calculator to find a model for the data.

x	1	2	3	4
y	30,624	32,436	34,167	35,989

x	5	6	7
y	37,684	39,311	41,098

1. Make a scatter plot. The points lie approximately on a _line_. This suggests a _linear_ model.

2. Use the _linear_ regression feature to find an equation of the model.

3. Graph the model along with the data to verify that the model fits the data well.

A model for the data is y = _1739x + 28,950_.

Deer Population An environmental group observes a deer population in a park where hunting has been banned. The table shows the population y counted x years after the ban began.

x	0	5	10	15	20
y	500	729	1271	2206	3765

Solution

1. Make a scatter plot. The points are level at first and then begin to _rise_ rapidly. This suggests an _exponential_ growth model.

2. Use the _exponential_ regression feature to find an equation of the model.

3. Graph the model along with the data to verify that the model fits the data well.

A model for the data is y = _468(1.11)^x.

Example 3

Use a quadratic model

Roller Coaster Riders A manager at a local amusement park kept a record of the number of people to ride the most popular roller coaster at the park. The table shows the number of people y that rode the roller coaster x hours after the park had opened. Use a graphing calculator to find a model for the data.

X	0	2	4	6	8	10	12
Y	85	163	282	341	398	381	304

Solution

1. Make a scatter plot. The points form an _inverted U-shape_. This suggests a _quadratic_ model.

2. Use the _quadratic_ regression feature to find an equation of the model.

3. Graph the model along with the data to verify that the model fits the data well.

A model for the data is y _-4.34x² + 73.7x + 62.8_.