The table gives actual and projected year-end assets in Social Security trust funds, in trillions of current dollars, where Year represents the number of years since 2000. The polynomial function defined by ƒ(x) = 0.0000329x³ - 0.00450x² + 0.0613x + 2.34 models the data quite well.

(a) To verify the fit of the model, find ƒ(10), ƒ(20), and ƒ(30).
(b) Use a graphing calculator with a command such as nDeriv to find the slope of the tangent line to the graph of ƒ at the following x-values: 0, 10, 20, 30, and 35.

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Year 10 20 30 40 50 Trillions of Dollars 2.45 2.34 1.03 -0.57 -1.86