Geometric Series Model For Wood Yield

Question

The table provides the annual wood yield from a sustainably managed forest, where the yield decreases by a constant percentage each year.

| Year | Wood Yield (cubic meters) |
|------|---------------------------|
| 1    | 2000                      |
| 2    | 1900                      |
| 3    | 1805                      |
| 4    | 1714.75                   |
| 5    | 1629.01                   |

If this trend continues, which of the following is the best estimate of the total wood yield, in cubic meters, over a 20-year period?

Accepted Answer

Approximately $$25,660$$ cubic meters, computed by $$2000 	imes \frac{1-0.95^{20}}{1-0.95}$$.

Answer

Approximately $$27,000$$ cubic meters, if wrongly assuming a faster decline rate.

Answer

Approximately $$24,000$$ cubic meters, which would be the result of a linear decline model.

Answer

Approximately $$20,000$$ cubic meters, if the decline rate only applied in the first year.

Geometric Series Model For Wood Yield

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