Fully stocked stands: This is a continuation . In this exercise we study one of the ingredients used in formulating the relation given in the preceding exercise among the stand-density index SDI, the number N of trees per acre, and the diameter D, in inches, of a tree of average size.34 This ingredient is an empirical relationship between N and D for fully stocked stands—that is, stands for which the tree density is in some sense optimal for the given size of the trees. This relationship, which was observed by L. H. Reineke in 1933, is
log N = −1.605 log D + k ,
where k is a constant that depends on the species in question.
a. Assume that for loblolly pines in an area the constant k is 4.1. If in a fully stocked stand the diameter of a tree of average size is 8 inches, how many trees per acre are there? (Round your answer to the nearest whole number.)
b. For fully stocked stands, what effect does multiplying the average size of a tree by a factor of 2 have on the number of trees per acre? ➞
c. What is the effect on N of increasing the constant k by 1 if D remains the same?