In the function \( f(x) = 23,000(0.92)^x \), the value \( 23,000 \) represents the initial value or the starting price of the new car at \( x = 0 \) years. This is the amount at which the car is valued when it is first purchased before any depreciation occurs. Therefore, \( 23,000 \) is the original price of the car.
The function f(x) = 23,000(0.92)^x shows how the value of a new car will depreciate over x years.
What does the 23,000 represent?
3 answers
what does the 0.92 respresent
In the function \( f(x) = 23,000(0.92)^x \), the value \( 0.92 \) represents the annual depreciation factor of the car's value. Specifically, it indicates that the car retains 92% of its value each year.
This means that every year, the value of the car is multiplied by \( 0.92 \), reflecting a depreciation of 8% per year (since \( 1 - 0.92 = 0.08 \) or 8%). Thus, the \( 0.92 \) factor shows how much of the car's value remains after each year.