2.4 – Using Linear Models

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)?

Example 2  The cost of producing 4 widgets is $ The cost of producing 8 widgets is $ 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? Predicting with Linear Models

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 meters and in 1987 its lean was meters. If the data is linear, find a model and use the model to predict how far the lean is in 2012.

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. XY Predicting with Linear Models

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. XY

Example 7  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. SizeEuropean Size