Chapter 5.4, Problem 19E

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

Quarterly Pine Pulpwood Prices In southwest Georgia, the average pine pulpwood prices vary predictably over the course of the year, primarily because of weather. Prices in $2009$ followed this pattern. At the beginning of the first quarter, the average price $P$ was $\$9$ per ton. During the first quarter, prices declined steadily to $\$8$ per ton, then remained steady at $\$8$ per ton through the end of the third quarter. During the fourth quarter, prices increased steadily from $\$8$ to $\$10$ per ton.

a. Sketch a graph of pulpwood prices as a function of the quarter in the year.

b. What formula for price $P$ as a function of $t$, the quarter, describes the price from the beginning of the year through the first quarter?

c. What formula for price $P$ as a function of $t$, the quarter, describes the price from the first to the third quarter?

d. What formula for price $P$ as a function of $t$, the quarter, describes the price from the third to the fourth quarter?

e. Write a formula for price $P$ throughout the year as a piecewise-defined function of $t$, the quarter.