Quarterly sawtimber prices: This is a continuation. In southwest Georgia, the average pine sawtimber prices vary predictably over the course of the year, primarily because of weather. From 1993...

Quarterly sawtimber prices: This is a continuation. In southwest Georgia, the average pine sawtimber 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 was $54 per ton. It decreased to $49 in the second quarter and then increased back to $54 for the third quarter, where it stayed through the fourth quarter.

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

b. Assume that 5t 2 accurately describes the shape of the curve during the first three quarters. Compose the function with an appropriate translation t − a for some a, and add a constant to the function to obtain a function P that describes the price throughout the three quarters.

c. What formula for price P describes the price during the third to fourth quarters?

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