Question 22 ( 4 points) Sarah bought her car for \( \$ 17,440 \). It is expected to depreciate an average of \( 14 \% \) each year during the first 6 years. What will the approximate value of her car be in 6 years? \( \$ 7056 \) \( \$ 7148 \) \( \$ 7236 \) \( \$ 7424 \)

To calculate the approximate value of Sarah's car after 6 years, we need to apply the depreciation formula. Each year, the car's value will decrease by 14%. So, after 1 year, the value will be: \[ \text{Value after 1 year} = 17440 \times (1 - 0.14) = 17440 \times 0.86 \approx 14910.40 \] We can continue this calculation for 6 years or use a formula for depreciation over multiple years: \[ \text{Value after } n \text{ years} = \text{Initial Value} \times (1 - \text{depreciation rate})^n \] Applying it for 6 years: \[ \text{Value after 6 years} \approx 17440 \times (0.86)^6 \approx 17440 \times 0.5410 \approx 9427.68 \] But there’s a mistake in the calculation above; let's do it stepwise correctly: 1. Year 1: \( 17440 \times 0.86 = 14910.40 \) 2. Year 2: \( 14910.40 \times 0.86 = 12807.74 \) 3. Year 3: \( 12807.74 \times 0.86 = 11054.64 \) 4. Year 4: \( 11054.64 \times 0.86 = 9506.99 \) 5. Year 5: \( 9506.99 \times 0.86 = 8176.01 \) 6. Year 6: \( 8176.01 \times 0.86 = 7031.45 \) So, the approximate value of her car in 6 years will be roughly **\( \$ 7056 \)**.