Cost of a Commodity The price p, in dollars, of a certaincommodity and the quantity x sold obey the demand equation-* + 200 0s x s 10001.Suppose that the cost C, in dollars, of producing x units is+ 40010Assuming that all items produced are sold, find the cost C asa function of the price p.

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Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.1: Polynomial Functions Of Degree Greater Than

Problem 63E

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Grazing Kangaroos The amount of vegetation eaten in a day by a grazing animal V of food available measured as biomass, in units such as pounds per acre. This relationship is called the functional response. If there is little vegetation available, the daily intake will be small, since the animal will have difficulty finding and eating the food. As the amount of food biomass increases, so does the daily intake. Clearly, though, there is a limit to the amount the animal will eat, regardless of the amount of food available. This maximum amount eaten is the satiation level. a.For the western grey kangaroo of Australia, the functional response is G=2.54.8e0.004V, where G=G(V) is the daily intake measured in pounds and V is the vegetation biomass measured in pounds per acre. i. Draw a graph of G against V. Include vegetation biomass levels up to 2000 pounds per acre. ii. Is the graph you found in part i concave up or concave down? Explain in practical terms what your answer means about how this kangaroo feeds. iii. There is a minimal vegetation biomass level below which the western grey kangaroo will eat nothing. Another way of expressing this is to say that the animal cannot reduce the food biomass below this level. Find this minimal level. iv. Find the satiation level for the western grey kangaroo. b. For the red kangaroo of Australia, the functional response is R=1.91.9e0.033V, Where R is the daily intake measured in pounds and V is the vegetation biomass measured in pounds per acre. i. Add the graph of R against V to the graph of G you drew in part a. ii. A simple measure of the grazing efficiency of an animal involves the minimal vegetation biomass level described above: The lower the minimal level for an animal, the more efficient it is at grazing. Which is more efficient at grazing, the western grey kangaroo or the red kangaroo?
Later High School Graduates This is a continuation of Exercise 16. The following table shows the number, in millions, graduating from high school in the United States in the given year. Year Number graduating in millions 2001 2.85 2003 2.98 2005 3.11 2007 3.24 a. Find the slope of the linear function modeling high school graduations, and explain in practical terms the meaning of the slope. b. Find a formula for a linear function that models these data. c. Express, using functional notation, the number graduating from high school in 2008, and then calculate the value. d. The actual number graduating from high school in 1994 was about 2.52 million. Compare this with the value given by the formula in part b and with your answer to part of Exercise 16. Which is closer to the actual value? In general terms, what was the trend in high school graduations from 1985 to 2007? 16. High School Graduates The following table shows the number, in millions, graduating from high school in the United States in the given year.16 Year Number graduating in millions 1985 2.83 1987 2.65 1989 2.47 1991 2.29 a. By calculating difference, show that these data can be modeled using a linear function. b. What is the slope for the linear function modeling high school graduations? Explain in practical terms the meaning of the slope. c. Find a formula for a linear function that models these data. d. Express, using functional notation, the number graduating from high school in 1994, and then use your formula from part c to calculate that value.

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Cost of a Commodity The price p, in dollars, of a certain commodity and the quantity x sold obey the demand equation -* + 200 0s x s 1000 1. Suppose that the cost C, in dollars, of producing x units is + 400 10 Assuming that all items produced are sold, find the cost C as a function of the price p.