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EXAMPLE 1

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. EXAMPLE 1. Use a linear model. Tuition.

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EXAMPLE 1

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

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

  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 EXAMPLE 1 Use a linear model STEP 3

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

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

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

  7. 1. SOLUTION f (x) = 0.0106x2 + 0.116x + 21.6 for Examples 1 and 2 GUIDED PRACTICE Use a graphing calculator to find a model for the data. Then graph the model and the data in the same coordinate plane.

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

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