The Problem

The data in the following table list natural gas consumption ( in quadrillion BTU) in the United States. Estimate the natural gas consumption in 1982.

Natural Gas Consumption
Year
1960
1970
1980
1990
1997
Consumption
12.4
21.8
20.4
19.3
22.6

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 L sub 1. Now press the RIGHT ARROW KEY so the cursor is in the L sub 2 column and enter the y-values (the consumption).

Screen Picture of TI-83 Calculator
Screen Picture of TI-83 Calculator
Screen Picture of TI-83 Calculator

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.

Screen Picture of TI-83 Calculator
Screen Picture of TI-83 Calculato
Screen Picture of TI-83 Calculato

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



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