To determine the approximate value of Bruce's car after 6 years, given that it depreciates at an average rate of 14% per year, we need to follow a step-by-step process:
1. Initial Value: Bruce bought his car for \[tex]$24,380.
2. Depreciation Rate: The car depreciates at an annual rate of 14%, which is represented as a decimal (0.14).
3. Number of Years: We need to calculate the car's value after 6 years.
4. Depreciation Calculation:
- Each year, the car's value is reduced by 14%. This means each year, the car retains 86% (100% - 14%) of its value.
- The retention rate each year is represented by \(1 - 0.14 = 0.86\).
5. Compound Depreciation Over 6 Years:
- To find the car's value after 6 years, we apply the depreciation rate repeatedly over the years.
Mathematically, we use the formula for compound depreciation:
\[ \text{Final Value} = \text{Initial Value} \times (\text{Retention Rate})^{\text{Number of Years}} \]
Substitute the known values into the formula:
\[ \text{Final Value} = 24380 \times (0.86)^6 \]
This calculation results in the approximate value of Bruce's car after 6 years.
Therefore, the approximate value of Bruce's car after 6 years is \$[/tex]9863.
Thus, the correct answer is:
\$9863
