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Price of Perfume The monthly demand for a certain brand of perfume is given by the demand equation p = 100e-0.0002x + 125 where p denotes the retail unit price (in dollars/bottle) and x denotes the quantity (in 1-oz bottles) demanded. (a) Find the rate of change of the price per bottle (in dollars) when x = 1,000 and when x = 3,000. (Round your answers to four decimal places.) X dollars/bottle X dollars/bottle x = 1,000 x = 3,000 (b) What is the price per bottle (in dollars) when x = 1,000? When x = 3,000? (Round your answers to the nearest cent.) x = 1,000 $ x = 3,000 $

College Algebra

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter3: Polynomial Functions

Section: Chapter Questions

Problem 104RE: Demand A company has found that the daily demand x for its boxes of chocolates is inversely...

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Transcribed Image Text:Price of Perfume The monthly demand for a certain brand of perfume is given by the demand equation -0.0002x p = 100e + 125 where p denotes the retail unit price (in dollars/bottle) and x denotes the quantity (in 1-oz bottles) demanded. (a) Find the rate of change of the price per bottle (in dollars) when x = 1,000 and when x = 3,000. (Round your answers to four decimal places.) x = 1,000 X dollars/bottle x = 3,000 dollars/bottle (b) What is the price per bottle (in dollars) when x = 1,000? When x = 3,000? (Round your answers to the nearest cent.) X = 1,000 2$ x = 3,000 $

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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?

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