Question

There are 24,000 square miles of forest in a western state. Forest fires decrease this area by 9.2% each year. The state needs to have more than 15,000 square miles of forest to keep their funding from a nonprofit wildlife organization.

Which inequality represents this situation, and if the fires continue to decrease the area of the forests at the same rate, will the state be able to keep their funding from the nonprofit wildlife organization in 5 years?



24,000(1.092)t > 15,000; no


24,000(0.092)t > 15,000; yes


24,000(0.908)t > 15,000; no


24,000(1.098)t > 15,000; yes

Answer 1

24,000(0.908)^t > 15,000; no

Explanation:

The multiplier each year is 100% - 9.2% = 90.8% = 0.908. There is only one answer choice with this as the yearly multiplier.

_____

In order to answer the yes/no question, we chose to rewrite the inequality as ...

24000·0.908^t -15000 > 0

The graph shows that is true for t < 4.87. In 5 years, the forest area will be below the minimum.