Question

A car that is purchased for $24,000 is expected to depreciate at a rate of 7% per year. If the function f(x) = abx models this situation, which function could be used to find the value of the car after 10 years?

A) f(x) = 24,000(0.93)10
B) f(x) = 24,000(0.07)10
C) f(x) = 24,000(1.07)10
D) f(x) = 24,000(10)1.93

Answer 1

Given that the original cost of the car is $24000 and it depreciates at the rate of 7%, the function that will represent the value of the car after 10 years will be given by:
f(x)=p(r)^t
where:
p=current cost
r=rate
t=time
but
p=24000, r=100-7=93%=0.93, t=10
thus the function that models the value of the car after 10 years is:
f(x)=24000(0.93)^10

Answer: A) f(x) = 24,000(0.93)^10