Question

Juan is purchasing a brand new Ford Mustang that costs $38,500. The car depreciates 12% annually. Which equation below can be used to determine the value of the car 5 years later?

a. (Y = 38500(0.12)ˣ)
b. (Y = 38500(0.88)ˣ)
c. (Y = 38500(12)ˣ)
d. (Y = 38500(1.12)ˣ)

Answer 1

The car's value after depreciation is calculated using an exponential decay function, with Y = 38500(0.88)^x being the correct formula to find the car's value after 5 years. Option b is thus the correct answer.

Step-by-step explanation:

To determine the value of a car that depreciates annually, we use the formula for exponential decay, where the original value of the car is multiplied by (1 - the rate of depreciation) raised to the power of the number of years passed. In this case, the car's original value is $38,500 and it depreciates at a rate of 12% annually. Therefore, the correct formula to find the value after 5 years would be:

Y = 38500(0.88)^x

So, the correct choice is option b: Y = 38500(0.88)^x. The 'x' in the equation represents the number of years after the purchase, which, for this scenario, would be '5'