The table shows U.S. gross domestic product (GDP) in billions of dollars for selected years from 2000 to 2070 (actual and projected).

Assume that the GDP can be modeled with the function

G(t) = 213(0.2t + 5)³ - 5020(0.2t + 5)² + 8810t + 104,000

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 2015 and 2025.

(b) Use the data in the table to find the average rate of change of the GDP from 2015 to 2025.

(c) How well does your answer from part (b) approximate the instantaneous rate of change of GDP in 2020?

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Year GDP Year GDP 2000 9143 2040 79,680 2005 12,145 2045 103,444 133,925 173,175 2010 16,174 2050 2015 21,270 2055 2020 27,683 2060 224,044 2025 35,919 2065 290,042 2030 46,765 2070 375,219 2035 61,100