A certain forest covers an area of \( 1900 \mathrm{~km}^{2} \). Suppose that each year this area decreases by \( 8.75 \% \). What will the area be after 8 years? Use the calculator provided and round your answer to the nearest square kilometer. \( \square \mathrm{km}^{2} \)

To find the area of the forest after 8 years, we can use the formula for exponential decay: \[ A = A_0 \times (1 - r)^n \] where: - \( A \) is the area after \( n \) years, - \( A_0 \) is the initial area, - \( r \) is the rate of decrease per year, - \( n \) is the number of years. Given: - Initial area \( A_0 = 1900 \, \text{km}^2 \), - Rate of decrease per year \( r = 8.75\% = 0.0875 \), - Number of years \( n = 8 \). Substitute the values into the formula: \[ A = 1900 \times (1 - 0.0875)^8 \] Now, we can calculate the area after 8 years using the calculator provided. Calculate the value by following steps: - step0: Calculate: \(1900\left(1-0.0875\right)^{8}\) - step1: Subtract the numbers: \(1900\times 0.9125^{8}\) - step2: Convert the expressions: \(1900\left(\frac{73}{80}\right)^{8}\) - step3: Simplify: \(1900\times \frac{73^{8}}{80^{8}}\) - step4: Rewrite the expression: \(20\times 95\times \frac{73^{8}}{80^{8}}\) - step5: Rewrite the expression: \(20\times 95\times \frac{73^{8}}{20^{8}\times 4^{8}}\) - step6: Reduce the numbers: \(95\times \frac{73^{8}}{20^{7}\times 4^{8}}\) - step7: Rewrite the expression: \(5\times 19\times \frac{73^{8}}{20^{7}\times 4^{8}}\) - step8: Rewrite the expression: \(5\times 19\times \frac{73^{8}}{5^{7}\times 4^{7}\times 4^{8}}\) - step9: Reduce the numbers: \(19\times \frac{73^{8}}{5^{6}\times 4^{7}\times 4^{8}}\) - step10: Multiply the fractions: \(\frac{19\times 73^{8}}{256000000\times 4^{8}}\) - step11: Expand the expression: \(\frac{19\times 73^{8}}{16777216000000}\) The area of the forest after 8 years will be approximately \( 913.31 \, \text{km}^2 \) when rounded to the nearest square kilometer.