GDP The scatterplot shows the gross domestic product (GDP)

Chapter 9, Problem 27E

(choose chapter or problem)

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^{\prime \prime} \times 4^{\prime \prime} a piece that is 12 feet long contains 8 board feet.) To estimate the amount of lumber in a log, buyers mea- sure the diameter inside the bark at the smaller end. Then they look at a table based on the Doyle Log Scale. The table below shows the estimates for logs 16 feet long.

\(\begin{array}{|l|rrrrrr|} \hline \text { Diameter of Log } & 8^{\prime \prime} & 12^{\prime \prime} & 16^{\prime \prime} & 20^{\prime \prime} & 24^{\prime \prime} & 28^{\prime \prime} \\ \text { Board Feet } & 16 & 64 & 144 & 256 & 400 & 576 \\ \hline \end{array}\)

a) What model does this scale use?

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?