Proportions of trees: Table 5.7 gives the diameter d and height h, both in feet, of some “champion” trees (largest American specimens) of a variety of shapes.31 (See Figure 5.67.) a. Make a plot of ln...

Proportions of trees: Table 5.7 gives the diameter d and height h, both in feet, of some “champion” trees (largest American specimens) of a variety of shapes.31 (See Figure 5.67.)

a. Make a plot of ln h against ln d.

b. Find a formula for the regression line of ln h against ln d, and add this line to the plot you found in part a.

 c. Which is taller for its diameter: the plains cottonwood or the weeping willow?

d. Find a formula that models h as a power function of d.

e. 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 d compare with this formula?

 ii. Are any of the trees in the table taller than their critical buckling height?