A laptop computer is purchased for \( \$ 2450 \). After each year, the resale value decreases by \( 35 \% \). What will the resale value be after 4 years? Use the calculator provided and round your answer to the nearest dollar. \( 5 \square \)

To find the resale value of the laptop after 4 years, we can use the formula for exponential decay: \[ V = P \times (1 - r)^n \] where: - \( V \) is the resale value after \( n \) years, - \( P \) is the initial purchase price, - \( r \) is the rate of decrease per year, - \( n \) is the number of years. Given: - Initial purchase price \( P = \$2450 \), - Rate of decrease per year \( r = 35\% = 0.35 \), - Number of years \( n = 4 \). Substitute the values into the formula: \[ V = 2450 \times (1 - 0.35)^4 \] Now, we can calculate the resale value after 4 years using the calculator provided. Calculate the value by following steps: - step0: Calculate: \(2450\left(1-0.35\right)^{4}\) - step1: Subtract the numbers: \(2450\times 0.65^{4}\) - step2: Convert the expressions: \(2450\left(\frac{13}{20}\right)^{4}\) - step3: Simplify: \(2450\times \frac{13^{4}}{20^{4}}\) - step4: Evaluate the power: \(2450\times \frac{28561}{20^{4}}\) - step5: Rewrite the expression: \(10\times 245\times \frac{28561}{20^{4}}\) - step6: Rewrite the expression: \(10\times 245\times \frac{28561}{10^{4}\times 2^{4}}\) - step7: Reduce the numbers: \(245\times \frac{28561}{10^{3}\times 2^{4}}\) - step8: Rewrite the expression: \(5\times 49\times \frac{28561}{10^{3}\times 2^{4}}\) - step9: Rewrite the expression: \(5\times 49\times \frac{28561}{5^{3}\times 2^{3}\times 2^{4}}\) - step10: Reduce the numbers: \(49\times \frac{28561}{5^{2}\times 2^{3}\times 2^{4}}\) - step11: Multiply: \(\frac{49\times 28561}{3200}\) - step12: Multiply: \(\frac{1399489}{3200}\) The resale value of the laptop after 4 years is approximately $437.34. Therefore, the resale value after 4 years is $437.34.