A certain forest covers an area of \( 3100 \mathrm{~km}^{2} \). Suppose that each year this area decreases by \( 9 \% \). What will the area be after 10 years? Use the calculator provided and round your answer to the nearest square kilometer.

To find the area of the forest after 10 years, we need to calculate the area after each year and then sum up the areas for 10 years. Given: - Initial area of the forest = \( 3100 \mathrm{~km}^{2} \) - Decrease in area each year = \( 9\% \) Let's calculate the area after each year and then sum up the areas for 10 years. Calculate the value by following steps: - step0: Calculate: \(3100\left(1-0.09\right)^{10}\) - step1: Subtract the numbers: \(3100\times 0.91^{10}\) - step2: Convert the expressions: \(3100\left(\frac{91}{100}\right)^{10}\) - step3: Simplify: \(3100\times \frac{91^{10}}{100^{10}}\) - step4: Rewrite the expression: \(100\times 31\times \frac{91^{10}}{100^{10}}\) - step5: Reduce the numbers: \(31\times \frac{91^{10}}{100^{9}}\) - step6: Multiply: \(\frac{31\times 91^{10}}{100^{9}}\) The area of the forest after 10 years will be approximately \( 1207.19 \mathrm{~km}^{2} \). Therefore, after 10 years, the area of the forest will be approximately \( 1207.19 \mathrm{~km}^{2} \).