Gross domestic product The table shows U.S. gross domestic product (GDP) in billions of dollars for selected years from 2000 to 2070 (actual and projected).
Year | GDP | Year | GDP |
2000 | 9143 | 2040 | 79,680 |
2005 | 12,145 | 2045 | 103,444 |
2010 | 16,174 | 2050 | 133,925 |
2015 | 21,270 | 2055 | 173,175 |
2020 | 27,683 | 2060 | 224,044 |
2025 | 35,919 | 2065 | 290,042 |
2030 | 46,765 | 2070 | 375,219 |
2035 | 61,100 |
Source: Social Security Administration Trustees Report
Assume the GDP can be modeled with the function
where G(t) is in billions of dollars and t is the number of years past 2000.
(a) Use the model to find and interpret the instantaneous rates of change of the GDP in 2005 and 2015.
(b) Use the data in the table to find the average rate of change of the GDP from 2005 to 2015.
(c) How well does your answer from part (b) approximate the instantaneous rate of change of GDP in 2010?
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