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Unformatted text preview: MATH 110 BUSINESS CALCULUS CHAPTER 2 NONLINEAR MODELS Section 2.1 Quadratic Function and Models 1. Sketch the graph of the quadratic functions, indicating the coordinates of the vertex the y‐intercept, and the x‐intercepts (if any): 2
(a) f ( x) = − x − x (b) f ( x) = x + 2 x + 1 2 2
(c) f ( x) = x − 10 x − 600 2. For the given demand function, express the total revenue R as a function of the price p per item, sketch the graph of the resulting function, and determine the price p that maximizes total revenue: (a) q = −3 p + 300 3. Fuel Efficiency The fuel efficiency (in miles per gallon) of an SUV (sport utility vehicle) depends on its weight according to the formula E = 0.0000016 x 2 − 0.01x + 54 (1800 ≤ x ≤ 5400) where x is the weight of an SUV in pounds. (a) According to the model, what is the weight of the least fuel‐
efficient SUV? (b) Would you trust the model for weights greater than the answer you obtained? Explain. 4. Revenue Pack‐Em‐In Real Estate is building a new housing development. The more houses it builds, the less people will be willing to pay, due to the crowding and smaller lot sizes. In fact, if it builds 40 houses in this particular development, it can sell them for $200,000 each, but if it builds 60 houses, it will only be able to get $160,000 each. (a) Obtain a linear demand equation and hence determine how many houses Pack‐Em‐In should build to get the largest revenue. (b) What is the largest possible revenue? 5. Finding the model from data The following table shows the number of research articles in Physics Review that were written by research in the U.S. in 1983, 1993, and 2003 (here t = 0 represents 1983). Year t
Science Articles (Hundreds) 0
42 Find a quadratic model for these data, and use your model to estimate the number of articles published in 1998. ...
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This note was uploaded on 10/19/2011 for the course MATH 110 taught by Professor Staff during the Spring '11 term at S.F. State.
- Spring '11