Source: US Department of Energy

a). Find a polynomial function of degree 3 that models the data.

Solution:
A model of degree 3 has been chosen since the data appears to have 2 turning points.

First clear all lists in the calculator. Press STAT and then 1:Edit. Enter the x-values (the years) in . Now press the RIGHT ARROW KEY so the cursor is in the column and enter the y-values (the consumption).

Press STAT, then the RIGHT ARROW KEY to select CALC , and then select 6:CubicReg for cubic regression. Make sure L1 and L2 appear for the Xlist and Ylist. In preparation for Part b) and Part c), scroll down to Store RegEQ: then press VARS, right-arrow to Y-VARS, then pres ENTER twice. A Y1 now appears. Arrow-down to Calculate and press ENTER once more.

Therefore, the polynomial function of degree 3 which models the data is: