Logs (not logarithms). Many professions use tables to determine key quantities. The value of a log is based on the number of board feet of lumber the log may contain.

(A board foot is the equivalent of a piece of wood 1 inch thick, 12 inches wide, and 1 foot long. For example, a 2 * 4 piece that is 12 feet long contains 8 board feet.)

To estimate the amount of lumber in a log, buyers measure the diameter inside the bark at the smaller end. Then they look in a table based on the Doyle Log Scale. The table below shows the estimates for logs 16 feet long.

Diameter of Log 8 12 16 20 24 28
Board Feet 16 64 144 256 400 576

a) What transformation of Board Feet makes this relationship linear?

b) Based on a linear regression using this transformation, How much lumber would you estimate that a log 10 inches in diameter contains?

c) What does this model suggest about logs 36 inches in diameter?