Question

Answered Only 77% of a car's value remains after each passing year. A new car is sold for $32,850. Which function represents the resale value of the car after x years?

A. \(f(x) = 32,850(1 - 0.23)^x\)

B. \(f(x) = 32,850(0.23)^x\)

C. \(f(x) = 32,850(1 + 0.23)^x\)

D. \(f(x) = 0.77(32,850)^x\)

Answer 1

The function that represents the resale value of the car after x years is f(x) = 32,850(1 - 0.23)^x.

Step-by-step explanation:

The resale value of the car after x years can be represented by the function: f(x) = 32,850(1 - 0.23)^x.

This function takes into account that after each passing year, only 77% of the car's value remains. To calculate the resale value after x years, we multiply the initial price of the car ($32,850) by the remaining percentage (1 - 0.23) raised to the power of x.

For example, if we want to find the resale value after 3 years, we can substitute x with 3 in the function: f(3) = 32,850(1 - 0.23)^3.