A construction science researcher is interested in evaluating the relationship between energy consumption by the homeowner and the difference between the internal and external temperatures. There were 30 homes used in the study. During an extended period of time, the ­average temperature difference (in ° F) inside and outside the homes was recorded. The average energy consumption was also recorded for each home. The data are given here with y = energy consumption and x = mean temperature difference. Plot the data and suggest a polynomial model ­between y and x.

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y 16 12 740 26 33 98 105 65 130 90 109 10 118 123 x 1 1 13 3 3 6 6 6 99 9 12 12 12 y 99 113 105 90 109 115 134 105 129 119 133 99 195 149 160 x 15 15 15 18 18 18 21 21 21 24 24 24 30 30 30