2 4 Using Linear Models ADVANCED ALGEBRA D

2. 4 – Using Linear Models ADVANCED ALGEBRA D

Modeling Real-World Data Example 1 A car enters the interstate 5 miles east of Lincoln. The car travels at an average speed of 70 mph. Write an equation for the distance d (miles) from Lincoln t hours after entering the interstate. § How long will it take the car to reach Omaha (53 miles from Lincoln)? §

Predicting with Linear Models Example 2 The cost of producing 4 widgets is $204. 80. The cost of producing 8 widgets is $209. 60. If the data is linear, find a model (equation). Use the model to predict how much it costs to produce 12 widgets. § What is the y-intercept? What does it mean about the production of the widgets? §

Example 3 § The cost of producing 100 books is $517 and the cost of producing 500 books is $1400. If the data is linear, find a model and use it to predict the cost of producing 1000 books.

Example 4 § In 1975 the Leaning Tower of Pisa’s lean was 2. 9641 meters and in 1987 its lean was 2. 9758 meters. If the data is linear, find a model and use the model to predict how far the lean is in 2012.

Predicting with Linear Models Example 5 Graph the data (on the calculator). Is a linear model reasonable? § If a linear model is reasonable, use the calculator to determine the linear model. § X Y 2 3. 5 4 4. 9 6 6. 3 8 4. 6 10 2. 9

Example 6 Graph the data (on the calculator). Is a linear model reasonable? § If a linear model is reasonable, use the calculator to determine the linear model. § X Y 1 2. 1 3 3. 1 5 4 7 5. 2 9 5. 9

§ § § The chart models shoe sizes in US vs. European sizing. Graph the data (on the calculator). Is a linear model reasonable? Estimate the European equivalent of a US 6. Use the calculator to find a linear model. Use the linear model to predict the European equivalent of a US 6. Use the linear model to predict the US equivalent of a European 48. U. S. Size European Size 1 31 3 34 5 36 7 39 9 41 11 44 Example 7