Question

The value of a car is $21,500. It loses 12% of its value every year. Show complete work.

(a) Write a function that represents the value y (in dollars) of the car after x years.

(b) Use the function to estimate the value of the car after 6 years. (round your answer to the nearest whole number)

Answer 1

The function is y=21500(1-0.12)ˣ, and the value after 6 years would be 9985.

The general form of the function is y=a×bˣ, where a is the initial value, b is the rate of increase (in this case, decrease) + 1, and x is the number of years.

Substituting 6 for x, we have:
y=21500(1-0.12)⁶=21500(0.88)⁶=9984.69≈9985.