Spreadsheets in

Mathematics Explorations

by Molly McKee

We can use a spreadsheet program to enter the data and generate a scatterplot.

We need to decide which function will give us the best-fitting line.

Linear: y=mx+b

Exponential: y=cebx

Power: y=cxb

We can test the accuracy of all three lines by using the functions with data points we already know:

Linear: y=1.7097x-77.859

Exponential: y=1.5703e0.03x

Power: y=0.0006x2.4926

Let x = 80.

The Linear equation yields 58.917.

The Exponential equation yields 17.310

The Power equation yields 33.250.

By the information given, we know that when the forest was 80 years old the lumber harvest was about 33 100s of board feet. The power equation is obviously the most accurate. We can now use this equation to guesstimate how much board feet of lumber can be harvested for a forest of any given age. Let’s assume a forest is 400 years old. Then 400 would be our x-value:

y = .0006(4002.4926)

y = 1836.733

Approximately 1837 100s of board feet could be harvested from a forest that is 400 years old.

Suppose you wanted to see how long you would need to wait to be able to harvest 400 100s of board feet from a forest. In other words, how old would a forest have to be to yield a harvest of approximately 400. In this case we would be solving for x, not y, and 400 would be our y-value:

400 = .0006(x2.4926)

666666.667 = x2.4926

217 = x

So when a forest is approximately 217 years old, the harvest of lumber should be about 400.