題組內容

1. Consider the case of a forester who must decide when to cut down a growing tree. Assuming that the value of the tree at any time, $t$, is given by $f(t)$ and that L dollars were invested initially as payments to workers who planted the tree. Assume also the continuous market interest rate is given by $r$. Suppose the trees grow according to the equation: $f(t) = e^{0.6\sqrt{t}}$, where $e$ is the base of natural logarithms.


(1) Please show the present discounted value (PDV) of the treeowner's profit when the tree is planted. \( (10\%) \)