To calculate the value of the car after 10 years, we can use the formula for exponential decay:
\[ V = P(1 - r)^t \]
where:
- \( V \) is the future value of the car,
- \( P \) is the initial value of the car,
- \( r \) is the annual depreciation rate (as a decimal),
- \( t \) is the time in years.
Given:
- \( P = 12329 \)
- \( r = 0.085 \)
- \( t = 10 \)
Substituting the values into the formula:
\[ V = 12329(1 - 0.085)^{10} \] \[ V = 12329(0.915)^{10} \]
Now, we calculate \( (0.915)^{10} \):
\[ (0.915)^{10} \approx 0.4138 \]
Now, we can substitute this back into the equation:
\[ V \approx 12329 \times 0.4138 \approx 5095.43 \]
Therefore, the value of the car after 10 years will be approximately $5095.43.