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Unformatted text preview: 9B: Linear Modeling Friday February 11, 2011 (continued) All functions in this section have domains and ranges consisting of numbers. Rate of Change Definition L linear function is a function with a constant fate of change. That is, for every unit increase in the independent variable, the change in the dependent variable is the same. The graph of a linear function is a straight line (hence the name “linear”). Definition For a linear function, the slope is the rate of change of the function. It is computed by dividing a change in dependent variable by the corresponding change in inde- pendent variable. Example 1. Consider the following graphs that give the position of a vehicle driving at a constant speed time (hrs) Distance (mi) 1 hr 2 hr 3 hr 4 hr 30 60 90 (2 , 30) (4 , 60) Distance (mi) 1 hr 2 hr 3 hr 4 hr 30 60 90 (1 , 30) (3 , 100) In the first graph, the slope is slope = rate of change = change in dependent variable change in independent variable = 30mi 2 hr = 15 mi hr Similarly, in the second graph the slope is slope = 70 mi 2hr = 35 . 5 mi hr 1 2 Example 2. Drawing a Linear Model Suppose you hike a 3-mile trail that has a starting elevation of 8000 ft. Every mile you hike the elevation increases by 650 ft. (a) What is the domain of the elevation function? Solution Since the independent variable is the distance hiked d , the independent variable is between 0 and 3. The domain is therefore ≤ d ≤ 3 (b) Draw the graph of a linear function that models the elevation as a function of distance hiked Solution (you draw) (c) Remark about the validity of this model. Solution Example 3. Price-Demand Function A store sells pineapples. Based on data for pineapples priced between $ 2 and $ 7, a linear model is created to describe how demand (the number of pineapples sold per day) varies with price. The graph of this linear model is given below Price ( $ ) # Pineapples Sold 2 3 4 5 6 7 8 9 10 (2 , 80) (5 , 50) 20 40 60 80 100 (a) What is the rate of change for this model?...
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This note was uploaded on 01/08/2012 for the course MGF 1107 taught by Professor Staff during the Spring '08 term at University of Florida.
- Spring '08