A certain forest covers an area of 2600 km2. Suppose that each year this area decreases by 7.75%. What will the area be after 12 years?Use the calculator provided and round your answer to the nearest square kilometer.km2

To solve this problem, we need to understand that the decrease of the forest area is a compound decrease. This means that each year, the forest decreases by 7.75% of the remaining forest area, not the original forest area.

Here are the steps to solve this problem:

1. Convert the percentage decrease to a decimal by dividing by 100. So, 7.75% becomes 0.0775.

2. Subtract this decimal from 1 to find the annual rate of decrease. So, 1 - 0.0775 = 0.9225. This means that each year, 92.25% of the forest remains.

3. Raise this rate to the power of the number of years to find the total decrease over that time period. So, 0.9225^12 = 0.3703. This means that after 12 years, 37.03% of the original forest area remains.

4. Multiply the original forest area by this percentage to find the remaining forest area. So, 2600 km^2 * 0.3703 = 962.78 km^2.

5. Round this to the nearest square kilometer to get the final answer. So, the forest area will be approximately 963 km^2 after 12 years.