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13112an1.7-12 - c Kendra Kilmer January 4 2012 Section 1.2...

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c circlecopyrt Kendra Kilmer January 4, 2012 Section 1.2 - Mathematical Models: A Catalog of Essential Functions A mathematical model is a mathematical description (often by means of a function or an equation) of a real-world phenomenon. The purpose of the model is to understand the phenomenon and perhaps to make predictions about future behavior. Defintion: A has the form y = f ( x )= mx + b where m is the slope and b is the y -intercept. For a linear function, the rate of change is constant, and thus the slope can be interpreted as the rate of change of y with respect to x . Example 1: Sales of CDs have declined since 1999. Sales were $938 . 2 million in 1999 and $745 . 9 million in 2003. a) Find a formula for sales, S , of CDs, in millions of dollars, as a linear function of the number of years, t , since 1999. b) Interpret the slope. c) Use the formula to predict CD sales in 2010. Example 2: Search and rescue teams work to find lost hikers. Members of the search team separate and walk parallel to one another. The table shows the percent, P , of lost individuals found for various separation distances, d . Separation distance d(ft) 20 40 60 80 100 Percent found, P 90 80 70 60 50 a) Explain how you know that P is a linear function. b) What is the slope of the linear function? Give units and interpret.
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