Stand density: Forest managers are interested in measures of how crowded a given forest stand is.33 One measurement used is the stand-density index, or SDI . It can be related to the number N of trees...

Stand density: Forest managers are interested in measures of how crowded a given forest stand is.33 One measurement used is the stand-density index, or SDI . It can be related to the number N of trees per acre and the diameter D, in inches, of a tree of average size (in terms of cross-sectional area at breast height) for the stand. The relation is

log SDI = log N + 1.605 log D − 1.605 .

a. A stand has 500 trees per acre, and the diameter of a tree of average size is 7 inches. What is the stand-density index? (Round your answer to the nearest whole number.)

b. What is the effect on the stand-density index of increasing the number of trees per acre by a factor of 10, assuming that the average size of a tree remains the same?

c. What is the relationship between the stand-density index and the number of trees per acre if the diameter of a tree of average size is 10 inches?