The following table gives the diameter d and height h, both in feet, of some "champion" trees (largest American specimens) of a variety of shapes.t Tree Diameter d Height h Plains cottonwood 2.9 80 Hackberry Weeping willow Ponderosa pine 5.7 113 6.2 95 8.6 162 Douglas fir 14.4 221 (a) Find a formula that models h as a power function of d. h = 38.43 x d0.61 h = 26.87 x ɖ0.57 h = 35.91 × ɖ0.66 h = 40.03 x d0.68 h = 31.93 x d0.71 (b) Which is taller for its diameter: the plains cottonwood or the weeping willow? O plains cottonwood O weeping willow (c) It has been determined that the critical height at which a column made from green wood of diameter d, in feet, would buckle under its own weight is 140d2/3 feet. (i) How does your answer to part (a) compare with this formula? The leading coefficient in our part (a) model is larger than 140. O The models are the same. Our model in part (a) used the units "yards". O The exponent in our part (a) model is larger than 2/3. The leading coefficient in our part (a) model is smaller than 140. (ii) Are any of the trees in the table taller than their critical buckling height? O Yes O No

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