Answer/Step-by-step explanation:
To find the value of the car after 11 years, we can use the formula for exponential decay:
V = P x (1 - r)^t
Where:
- V is the final value of the car after t years
- P is the initial purchase price of the car
- r is the annual depreciation rate (as a decimal)
- t is the number of years
Given:
- P = $20,700
- r = 11% = 0.11 (as a decimal)
- t = 11
Substitute the values into the formula:
V = 20700 x (1 - 0.11)^11
V = 20,700 x (0.89)^11
Now, calculate the value:
V = x 0.356032498
V ≈ 7374.666847
To the nearest cent, the value of the car after 11 years would be approximately $7374.67.
