The depreciation of a vehicle at a rate of 11% per year means that after one year, the vehicle's value will be 89% of its value at the start of that year (since 100% - 11% = 89%). This means the value of the vehicle will decrease by multiplying its current value by 0.89 each year.
The correct equation to model the situation is:
\[ f(x) = 45,000(0.89)^x \]
This equation indicates that after \( x \) years, the value \( f(x) \) of the vehicle will be equal to the initial purchase price of $45,000 multiplied by \( 0.89 \) raised to the power of \( x \), which correctly represents the depreciation at a rate of 11% per year.
So, the correct answer is:
f(x) = 45,000(0.89)^x