QD 87. Oil Production The following table shows the amount of crude oil (in billions of barrels) produced in the United States in recent years. Source: U.S. Energy Information Administration.
Year | Crude Oil Produced |
2004 | 1.986 |
2005 | 1.891 |
2006 | 1.857 |
2007 | 1.853 |
2008 | 1.825 |
2009 | 1.954 |
2010 | 1.997 |
2011 | 2.063 |
2012 | 2.368 |
2013 | 2.716 |
In this exercise we are interested in the total amount of crude oil produced over the 9-ycar period from mid-2004 to mid-2013, using the data for the 10 years above.
(a) One approach is to sum up the numbers in the second column, hut count only half of the first and last numbers. Give the answer to this calculation.
(b) Approximate the amount of crude oil produced over the 9-year period 2004-2013 by taking the average of the left endpoint sum and the right endpoint sum. Explain why this is equivalent to the calculation done in part (a).
(c) Explain why the answer from part (a) is the same as that obtained using the trapezoidal rule to approximate the amount of crude oil produced over the 9-vear period 2004–2013.
(d) Find the equation of the least squares line for this data, letting t = 0 correspond to 2000. Then integrate this equation over the interval [4, 13] to estimate the amount of crude oil produced over this time period. Compare with your answer to part (a).
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Finite Mathematics and Calculus with Applications
- Oil ProductionThe following table shows the amount of crude oil in billions of barrels produced in the United States in recent years. Source: U.S. Energy Information Administration. Year Crude Oil Produced 2002 2.097 2003 2.060 2004 1.989 2005 1.893 2006 1.857 2007 1.853 2008 1.830 2009 1.954 2010 2.000 2011 2.063 2012 2.377 In this exercise we are interested in the total amount of crude oil produced over the 10-year period from mid-2002 to mid-2012, using the data for the 11 years above. One approach is to sum up the numbers in the second column, but only count half of the first and last numbers. Give the answer to this calculation. Approximate the amount of crude oil produced over the 10-year period 2002-2012 by taking the average of the left endpoint sum and the right endpoint sum. Explain why this is equivalent to the calculation done in part a. This is also equivalent to a formula known as the trapezoidal rule, discussed in the next chapter. If your calculator has a cubic regression feature, find the best-fitting cubic function for these data, letting t=0 correspond to 2000. Then integrate this equation over the interval [2.12] to estimate the amount of crude oil produced over this time period. Compare with your answer to part a.arrow_forwardUse this data for the exercises that follow: In 2013, there were roughly 317 million citizens in the United States, and about 40 million were elderly (aged 65 and over).[34] 60. It is predicted that by 2030, one in five U.S. citizens will be elderly. How much greater will the chances of meeting an elderly person be at that time? What policy changes do you foresee if these statistics hold true?arrow_forward
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