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 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.

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

b) 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?

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