Chapter 2.6, Problem 1TU

TEST YOUR UNTERSTANDING FOR EXAMPLE 2.12

Replace the growth formula in the example by $G=40A^{-2}{e}^{11-40A^{-1}}$. At what age is growth maximized? What is the maximum growth rate?

In forestry management, it is important to know the growth and the yield of a forest stand. The growth G is the amount by which the volume of wood will increase in a unit of time, and the yield Y is the total volume of wood. A forest manager has determined that in a certain stand of age A, the growth $G=G\left(A\right)$ is given by the formula

$G=32A^{-2}{e}^{10-32A^{-1}}$

And the yield $Y=Y\left(A\right)$ is given by the formula

$Y=e^{10-32A^{-1}}$

Here G is measured in cubic feet per acre per year, Y in cubic feet per acre, and A in years.

Part 1 Draw a graph of growth as a function of age that includes ages up to 60 years.

Part 2 At what age is growth maximized?