the yield V (in millions of cubic ft per acre) for a forest at age t years is given by:

v = 6.7e^-48.1 / t

(b) determine the horizontal asymptote and interpret its meaning in the context of the problem.

(c) find the time necessary to obtain a yield of 1.3 million cubic feet.

could some provide with steps to solving this problem. mainly finding the asymptote.

## Answers (1)

I wish this client had a way to draw graphs so you could look at the graph of the function. The horizontal asymptote is the line the graph gets closer and closer to as t goes to ∞ .

It turns out that as t approaches infinity the

ratio -48.1/t approaches zero. That means

e to the -48.1/t approaches e^0 which is ONE.

Consequently v approaches 6.7 times 1 so

v=6.7 is the horizontal asymptote. Note that if

we were using x and y as our variables , that would be y=6.7 on the xy coordinate plane.

The interpretation is that as the age of the forest increases, the yield increases but at a diminishing rate until it reaches very near limiting value of 6.7 million cubic feet per acre.

To do part c we simply solve

6.7e^(-48.1/t) = 1.3 for unknown t

divide both sides by 6.7 so

e^(-48.1/t) = 1.3/6.7

so -48.1/t = ln(1.3/6.7)

t= -48.1/ln(1.3/6.7)