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 20 × 40 piece that’s 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 the amount of lumber in logs 36 inches in diameter?

Transcribed Image Text:

20" 28" Diameter of Log 8" 16 64 12" 16" 24" Board Feet 256 114 400 576