3. You buy a car for \( \$ 8000 \) that depreciates at a rale of \( 11 \% \) a year. How much is the car worth alter 5 years? \[ f(x)=8000(1-0.11)^{5}= \]

Calculate or simplify the expression \( 8000(1-0.11)^{5} \). Calculate the value by following steps: - step0: Calculate: \(8000\left(1-0.11\right)^{5}\) - step1: Subtract the numbers: \(8000\times 0.89^{5}\) - step2: Convert the expressions: \(8000\left(\frac{89}{100}\right)^{5}\) - step3: Simplify: \(8000\times \frac{89^{5}}{100^{5}}\) - step4: Rewrite the expression: \(1000\times 8\times \frac{89^{5}}{100^{5}}\) - step5: Rewrite the expression: \(10^{3}\times 8\times \frac{89^{5}}{10^{10}}\) - step6: Reduce the numbers: \(8\times \frac{89^{5}}{10^{7}}\) - step7: Rewrite the expression: \(8\times \frac{89^{5}}{2^{7}\times 5^{7}}\) - step8: Rewrite the expression: \(2^{3}\times \frac{89^{5}}{2^{7}\times 5^{7}}\) - step9: Reduce the numbers: \(1\times \frac{89^{5}}{2^{4}\times 5^{7}}\) - step10: Multiply the fractions: \(\frac{89^{5}}{16\times 5^{7}}\) The car is worth approximately $4467.25 after 5 years.