What does the 23,000 represent?

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

the number of years the car has been driven.

the starting value of the car.

the annual rate at which the car depreciates.

the decay factor.

1 answer

In the function \( f(x) = 23,000 (0.92)^x \), the value 23,000 represents the starting value of the car. This is the initial value from which the car's depreciation is calculated.

To clarify the other options:

  • The number of years the car has been driven is represented by \( x \).
  • The annual rate at which the car depreciates is 8% (since \( 1 - 0.92 = 0.08 \)), but that is not represented directly in the equation.
  • The decay factor is \( 0.92 \), which indicates that the car retains 92% of its value each year.

Thus, the correct answer is: the starting value of the car.