The value of a brand new SUV is currently $15,400. After every year, the value of the SUV decreases by 10%.
a)First construct an exponential decay equation:
(A) V = 15400(1 – 10)t
(B) V = 15400(1 – 0.10)t
(C) V = 15400(0.10)t
(D) V = 15400(10 – 0.10)t
b) When will the value of the SUV be $12,465?
t =
(A) 1 year
(B) 2 years
(C) 3 years
(D) 4 years
a)An exponential decay function has the form y = a(1 – r)t, where y is the final value, a is the initial value, r is the rate of decay in decimal form, and t is the time variable.
In this case, a = 15,400, and r = 0.10. So V = 15400(1 – 0.10)t . The correct answer is (B).
b) Graphing the equation, we see that y reaches a value of 12465 at t = 2 years.