To model the depreciation of the car, we can use the exponential decay formula. The value of the car after \( t \) years can be calculated using the formula:
\[ y = P(1 - r)^t \]
where:
- \( y \) is the value of the car after \( t \) years,
- \( P \) is the initial value of the car,
- \( r \) is the depreciation rate (in decimal form),
- \( t \) is the number of years.
Given:
- The initial cost of the car \( P = 15,000 \)
- The depreciation rate \( r = 21% = 0.21 \)
The equation becomes:
\[ y = 15000(1 - 0.21)^t \]
This simplifies to:
\[ y = 15000(0.79)^t \]
So the function to model the value of the car after \( t \) years is:
\[ y = 15000(0.79)^t \]