What does the .92 represent?

Question

the function f (x) = 23,000(0.92)
shows how the value
of a new car will depreciate over x years

the annual rate at which the car depreciates.

the starting value of the car.

the number of years the car has been driven.

the decay factor.

Answer 1

In the context of the function \( f(x) = 23,000(0.92^x) \), the value of \( 0.92 \) represents the decay factor.

This means that each year, the value of the car is multiplied by \( 0.92 \), indicating that it retains \( 92% \) of its value from the previous year. Thus, it depreciates at an annual rate of \( 8% \) (since \( 1 - 0.92 = 0.08 \)).

So, the correct answer is the decay factor.