Practice!

Sample Problem

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

Solution

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). The correct answer is (B).

b) Graphing the equation, we see that y reaches a value of 12465 at t = 2 years.