The value of a certain vehicle depreciates at a rate of 11% per year. If the initial purchase price of the vehicle was $45,000, which of the following equations is an accurate model of the situation

f(x)=45,000(0.11)^x
f(x)=45,000(0.89)^x
f(x)=45,000(1.11)^x
f(x)=45,000(11)^x

1 answer

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