A car is purchased for $24,000 . Each year it loses 30% of its value. After how many years will t

A car is purchased for $24,000 . Each year it loses 30% of its value. After how many years will the car be worth $7300 or less? (Use the calculator provided if necessary.) Write the smallest possible whole number answer.

Set up the depreciation equation D(t) where t is the number of years in the life of the car:
D(t) = 24,000/(1.3)^t

The problem asks for D(t)<=7300
24,000/(1.3)^t = 7300

Cross multiply:
7300(1.3)^t = 24,000

Divide each side by 7300
1.3^t = 24000/7300
1.3^t = 3.2877

Take the natural log of both sides:
LN(1.3^t) = LN(3.2877)

Using the natural log identities, we have:
t * LN(1.3) = 1.1902
t * 0.2624 = 1.1902

Divide each side by 0.2624
t = 4.5356
Rounding this up, we have t = 5