Chapter 4.5, Problem 17E

Reminder Round all answers to two decimal places unless otherwise indicated.

Stand Density Forest managers are interested in measures of hot crowed a given forest is. 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 $7\text{inches}$. 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 $10\text{inches}$?