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(a)
To calculate: The instantaneous rate of change of the GDP in 2005 and 2015 and interpret it. The table shows U.S. gross domestic product (GDP) in billions of dollars for selected years from 2000 to 2070. Assume that the GDP can be modeled with the function
(b)
To calculate: The average rate of change of the GDP from 2005 to 2015 using the data given. The table shows U.S. gross domestic product (GDP) in billions of dollars for selected years from 2000 to 2070. Assume that the GDP can be modeled with the function
(c)
The wellness of average rate of change of the GDP from 2005 to 2015 approximates the instantaneous rate of change of GDP in 2020. The table shows U.S. gross domestic product (GDP) in billions of dollars for selected years from 2000 to 2070. Assume that the GDP can be modeled with the function
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Chapter 9 Solutions
MATHEMATICAL APPL...(LL)-PKG.>CUSTOM<
- 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_forwardTable 6 shows the year and the number ofpeople unemployed in a particular city for several years. Determine whether the trend appears linear. If so, and assuming the trend continues, in what year will the number of unemployed reach 5 people?arrow_forward
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