To express the depreciation of the car as an exponential function, we can use the formula:
\[ V(t) = V_0 \times (1 - r)^t \]
where:
- \( V(t) \) is the value of the car after \( t \) years,
- \( V_0 \) is the initial value of the car,
- \( r \) is the depreciation rate,
- \( t \) is the number of years.
In this case:
- \( V_0 = 7565 \) (the purchase price of the car),
- \( r = 0.14 \) (the depreciation rate of 14%),
- \( t = 6 \) (the number of years).
Putting these values into the formula gives:
\[ V(t) = 7565 \times (1 - 0.14)^t \]
This simplifies to:
\[ V(t) = 7565 \times (0.86)^t \]
Now, we want to find the value of the car after 6 years, so we set \( t = 6 \):
\[ V(6) = 7565 \times (0.86)^6 \]
Calculating \( (0.86)^6 \):
\[ (0.86)^6 \approx 0.5277 \]
Now, substituting this back into our equation:
\[ V(6) \approx 7565 \times 0.5277 \approx 3994.48 \]
Thus, the worth of the car after 6 years is approximately $3,994.48.