The following table gives the value (in billions of dollars) of U.S. industrial shipments for selected years from 2014 and projected to 2040.

(a) Find a cubic function that models these data, with x as the number of years after 2010 and y as the billions of dollars of U.S. industrial shipments. Report your model with two significant digit coefficients.

(b) Use the reported model to find the point at which the rate of change of the value of U.S. industrial shipments begins to increase.

(c) Interpret the result found in part (b).

(d) What feature of the graph corresponds to the point found in part (b)?

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Year Value ($ billions) Year Value ($ billions) 2014 7.17 2029 9.62 2017 7.78 2032 10.04 2020 8.35 2035 10.56 2023 8.84 2038 11.11 2026 9.26 2040 11.48