Final answer:
Darnell's father can permit the timber company to harvest 500 cubic feet of wood per year, which is the forest's yearly growth, to maintain the ecosystem's size.
Step-by-step explanation:
how much Darnell's father could allow the timber company to cut each year while still maintaining the same size ecosystem is 500 cubic feet.
The explanation for this is based on an understanding of sustainable resource management. If the forest is growing at a rate of 500 cubic feet per year, then that is the maximum amount that can be harvested while still keeping the forest's size constant. This concept is critical, as it ensures that the ecosystem's health is not compromised by overexploitation. Over-cutting beyond the forest's regrowth rate would lead to degradation and a reduction in forest size over time, just like what has happened in some parts of the world where logging has gone uncontrolled, as evidenced by the information provided related to the Brazilian Amazon and the ITTO.
To maintain the same size ecosystem, Darnell's father should allow the timber company to cut a maximum of 500 cubic feet each year. This is because the forest grows at a rate of 500 cubic feet per year, and if the timber company cuts more than that, it will result in a decrease in the size of the ecosystem over time.