To determine the value of the car after \( t \) years taking into account a depreciation of 9% each year, we can use the formula for exponential decay.
The value of the car after \( t \) years, \( C(t) \), can be expressed as:
\[ C(t) = P \times (1 - r)^t \]
where:
- \( P \) is the initial value of the car (in this case, $28,000),
- \( r \) is the rate of depreciation (in this case, 0.09), and
- \( t \) is the number of years.
Substituting the values into the equation, we have:
\[ C(t) = 28000 \times (1 - 0.09)^t \]
This simplifies to:
\[ C(t) = 28000 \times (0.91)^t \]
So, the equation \( C(t) = 28000 \times (0.91)^t \) can be used to determine the value of the car after \( t \) years.
If you have options A, B, C, and D provided in your question, you should look for the equation that matches or is similar to \( C(t) = 28000 \times (0.91)^t \).
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