Question

A car is purchased for $45,000. Each year it loses 20% of its value. After how many years will the car be worth $14,500 or less?

Answer 1

6 years

Explanation:

D(t) = 45,000/(1.2)^t

D(t) <= 14,500

45,000/(1.2)^t = 14,500

cross multiply

(1.2)^t = 45,000/14,500

(1.2)^t = 3.1034

natural log of both sides

LN(1.2^t) = LN(3.1034)

t * LN(1.2) = 1.1325

t * 0.1823 = 1.1325

t = 6.2123

round up whole number = t = 6