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EXAMPLE 1 Use a linear model Tuition The table shows the average tuition y (in dollars) for a private four-year college in the United States from 1995 to 2002, where x is the number of years since 1995. Use a graphing calculator to find a model for the data.

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EXAMPLE 1 Use a linear model SOLUTION STEP 1 Make: a scatter plot. The points lie approximately on a line. This suggests a linear model. STEP 2 Use: the linear regression feature to find an equation of the model.

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EXAMPLE 1 Use a linear model STEP 3 Graph: the model along with the data to verify that the model fits the data well. A model for the data is y = 933x + 14,600. ANSWER

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EXAMPLE 2 Use an exponential model Cooling Rates You are storing leftover chili in a freezer. The table shows the chili’s temperature y (in degrees Fahrenheit) after x minutes in the freezer. Use a graphing calculator to find a model for the data.

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EXAMPLE 2 Use an exponential model SOLUTION STEP 1 Make: a scatter plot. The points fall rapidly at first and then begin to level off. This suggests an exponential decay model. STEP 2 Use: the exponential regression feature to find an equation of the model.

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EXAMPLE 2 Use an exponential model SOLUTION STEP 3 Graph: the model along with the data to verify that the model fits the data well. A model for the data is y = 98.2(0.969) x.ANSWER

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GUIDED PRACTICE for Examples 1 and 2 Use a graphing calculator to find a model for the data. Then graph the model and the data in the same coordinate plane. 1. f (x) = 0.0106x 2 + 0.116x + 21.6 SOLUTION

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GUIDED PRACTICE for Examples 1 and 2 2. f (x) = 12.2x + 30.3 SOLUTION

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© Boardworks 2012 1 of 9 Regression. © Boardworks 2012 2 of 9 Choosing a function type When we find the equation of the line of best fit for a scatter.

© Boardworks 2012 1 of 9 Regression. © Boardworks 2012 2 of 9 Choosing a function type When we find the equation of the line of best fit for a scatter.

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