To find the value of the motorcycle after 7 years using the given depreciation function \( y = 14,000(1 - 0.09)^x \), we plug in \( x = 7 \):
\[ y = 14,000(1 - 0.09)^7 \]
Calculating \( 1 - 0.09 \):
\[ 1 - 0.09 = 0.91 \]
Now we calculate \( 0.91^7 \):
\[ 0.91^7 \approx 0.5132 \quad (\text{using a calculator}) \]
Now, substitute this back into the function:
\[ y = 14,000 \times 0.5132 \approx 7,196.80 \]
Rounding to the nearest dollar, we get:
\[ y \approx 7,197 \]
None of the given options match this value, but it seems to be similar to the closest option, which is \( $7,235 \).
If we choose the provided options, the value after 7 years is approximately closest to:
$7,235.
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