Chapter 1.3, Problem 15E

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

Cutting Trees In forestry management, it is important to know the net stumpage value of a stand (that is, a group) of trees. This is the commercial value of the trees minus the costs of felling, hauling, etc. The graph in Figure $1.39$ shows the net stumpage value V, in dollars per acre, of a Douglas fir stand in the Pacific Northwest as a function of the age t, in years, of the stand.”

FIGURE $1.39$ Net stumpage value of a Douglas Fir

a. Estimate the net stumpage value of a Douglas fir 1 stand that is $60$ years old.

b. Estimate the age of a Douglas fir stand whose net stumpage value is $\$40,000\text{ per acre}$.

c. At what age does the commercial value of the stand equal the costs of felling, hauling, etc.?

d. At what age is the net stumpage value increasing the fastest?

e. This graph shows V only up to age $t=160\text{ years}$, but the Douglas fir lives for hundreds of years. Draw a graph to represent what you expect for V over the life span of the tree. Explain your reasoning.