Quarterly pine pulpwood prices: In southwest Georgia, the average pine pulpwood prices vary predictably over the course of the year, primarily because of weather. From 1993 through 1997, prices followed a similar pattern. In the first quarter of each year, the average price P was $18.50 per ton. It decreased at a steady rate to $14 in the second quarter and then increased at a steady rate up to $18 by the fourth quarter.
a. Sketch a graph of pulpwood prices as a function of the quarter in the year.
b. What type of function is P from the first to the second quarter?
c. What formula for price P as a function of t, the quarter, describes the price from the first to the second quarter?
d. What type of function is P from the second to the fourth quarter?
e. What formula for price P as a function of t, the quarter, describes the price from the second to the fourth quarter?
f. Write a formula for price P throughout the year as a piecewise-defined function of t, the quarter.