Let's look at some information in a spreadsheet and analyze the data.
This data is from the lumber industry, giving the approximate number of board feet per tree in a forest of a given age.
| Tree Data | |
| Age of Tree | 110s Board Feet |
| 20 | 1 |
| 40 | 6 |
| 60 | |
| 80 | 33 |
| 100 | 56 |
| 120 | 88 |
| 140 | |
| 160 | 182 |
| 180 | |
| 200 | 320 |
Tree Data
What function will fit this graph?
This equation and graph is getting close to the graph of the tree data. Only, the graph increases too quickly once x reaches 100. We need the graph to increase much more slowly.
This graph looks more like the function we want; however, we must remember that x can only be greater than or equal to 0.
By looking at the graph, we can estimate the number of board feet per tree for ages that have not been provided. Our data does not give the number of board feet for 60 years, 140 years, or 180 years.
From the graph, I would guess that 24 board feet could be cut from a tree 60 years old. I would estimate that 150 board feet could be cut from a tree 140 years old, and I would guess that 246 board feet could be cut from a tree 180 years old.
To follow the graph more closely click here.