Answer:
4.62 years
Step-by-step explanation:
Half the car's value =>$24,000/2 = $12,000
The formula for exponential decrease =
y = a(1 - r)^t
y = Initial value = $24,000
a = Value after time t = $12,000
r = Decrease rate = 15% = 0.15
t = time in years =??
Hence,
24,000 = 12000 ( 1 - 0.15)^t
Divide both sides by 12000
24000/12000 = 12000 ( 0.85)^t/ 12000
2 = 0.85^t
We take the logarithm of both sides
log 2 = log (0.85)^t
log 2 = t log 0.85
Divide both sides by log 0.85
t = log 2/log 0.85
t = 4.62098120373 years
Approximately = 4.62 years
It would take 4.62 years to be worth half the initial price
