Students in a lab measured the breaking strength S (in pounds) of wood 2 inches thick, x inches high, and 12 inches long. The results are shown in the table. x 4 6 8 10 12 2,505 5,815 10,659 16,693 24,317 (a) Use the regression capabilities of a graphing utility to fit a quadratic model to the data. (Round your coefficients to three decimal places.) S(x)= (b) Use a graphing utility to plot the data and graph the model. 140 120 S 100 80 60 40 20 25000 S 20000 15000 10000 5000 X 2 4 6 8 10 12 4 6 8 10 12 20000 15000 10000 5000 20000 15000 10000 5000 x 2 4 6 8 10 12 x 2 4 6 8 10 12 (c) Use the model to approximate the breaking strength when x = 2. (Round your answer to three decimal places.) 1.771 x lb (d) How many times greater is the breaking strength for a 4-inch-high board than for a 2-inch-high board? (Round your answer to two decimal places.) 1.41 (e) How many times greater is the breaking strength for a 12-inch-high board than for a 6-inch high board? (Round your answer to two decimal places.) 1.68 When the height of the board increases by a factor, does the breaking strength increase by the same factor? Explain. When the height is ---Select---, the breaking strength increases approximately by a factor of -?--