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Crude Oil Prices The price per barrel of crude oil in constant 2008 dollars can be approximated by
Where t is time in years since the start of 1980.48
a. What, in constant 2008 dollars, was the average rate of change of the price of oil from the start
b. Your answer to part (a) is quite small. Can you conclude that the price of oil hardly changed all over the 25-year period 1981-2006? Explain.
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Applied Calculus
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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?arrow_forwardInflation Assuming that the annual rate of inflation averages 4 over the next 10 years, the approximate costs C of goods or services during any year in that decade can be modeled by Ct=P1.04t, where t is the time in years and P is the present cost. The price of an oil change for your car is presently $29.88. Estimate the price 10 years from now.arrow_forward
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