APPLICATIONS #1: AVERAGE RATE OF CHANGE- INSTANTANOF CHANGE1. The management of the Titan Tire Company has determined that the weekly demandfunction for their Super Titan tires is given byp= f(x)=144- x where p is the price of tires measured in dollars and x is the%3D%3Ddemand measured in units of a thousand.A. Find the price when 5000 tires are sold. (x = 5)B. Find the price when 6000 tires are sold. (x = 6)C. Find p(6) - p(5)p(6)- p(5)f(x+ Ax) - f(x)D. FindThis is6-5AxThis value is the average rate of change of the unit price of a tire, or the marginal rate ofchange of the price.Following the outline above: (remember, tires are in units of 1000!) Show all of yourcomputational steps.A. Find the average rate of change between 5000 and 5100 tires.B. Find the average rate of change between 5000 and 5010 tires.Interpret your results.Find the instantaneous rate of change per 1000 tires. (This is f '(x))Interpret the results and compare this with your previous answer.The temnerature T of a person during an illness is given by

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Answered: APPLICATIONS #1: AVERAGE RATE OF…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.6: Quadratic Functions

Problem 50E

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Flood Control A river is 8 feet above its flood stage. The water is receding at a rate of 3 inches per hour. Write a mathematical model that shows the number of feet above flood stage after t hours. Assuming the water continually recedes at this rate, when will the river be 1 foot above its flood stage?
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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