To model the depreciation of Patricia's car, we can use the formula for exponential decay:
\[ V(t) = V_0 (1 - r)^t \]
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 (expressed as a decimal).
- \( t \) is the number of years.
Given:
- \( V_0 = 18,995 \)
- \( r = 0.18 \)
- We want to find \( V(6) \) for \( t = 6 \).
Plugging in the values:
\[ V(6) = 18,995 \times (1 - 0.18)^6 \]
Simplifying the equation:
\[ V(6) = 18,995 \times (0.82)^6 \]
Now, calculate \( (0.82)^6 \):
\[ (0.82)^6 \approx 0.384432 \]
Now multiply by the initial value:
\[ V(6) \approx 18,995 \times 0.384432 \approx 7,292.36 \]
Thus, the value of the car after 6 years is approximately $7,292.36.