You are the business manager of P. Bunyan Forests, Inc., and are trying to decide when you should cut your trees. The market value of the lumber that you will get if you let your trees reach the age of t years is given by the function W(t) = e.20t−.001t2 . Mr. Bunyan can earn an interest rate of 5% per year on money in the bank. The rate of growth of the market value of the trees will be greater than 5% until the trees reach 75 years of age. (Hint: It follows from elementary calculus that if F (t) = eg (t), then F` (t)/F (t) = g` (t).)
(a) If he is only interested in the trees as an investment, how old should Mr. Bunyan let the trees get?
(b) At what age do the trees have the greatest market value?