To find the value of the car after 5 years of depreciation at a rate of 5.75% per year, we can use the formula for exponential decay:
\[ V = P(1 - r)^t \]
where:
- \( V \) is the future value of the car,
- \( P \) is the initial purchase price of the car,
- \( r \) is the annual depreciation rate (as a decimal),
- \( t \) is the time in years.
Given:
- \( P = 16500 \) dollars,
- \( r = 5.75% = 0.0575 \),
- \( t = 5 \) years.
Now plug in the values:
\[ V = 16500(1 - 0.0575)^5 \]
Calculate \( 1 - 0.0575 \):
\[ 1 - 0.0575 = 0.9425 \]
Now calculate \( 0.9425^5 \):
\[ 0.9425^5 \approx 0.7354 \quad (\text{using a calculator}) \]
Now substitute this value back into the equation:
\[ V = 16500 \times 0.7354 \approx 12151.10 \]
Finally, rounding to the nearest cent, the value of the car after 5 years will be approximately:
\[ \boxed{12151.10} \text{ dollars} \]
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