Every year, a car loses 15% of the value it had the year before. If the car's initial value is $ 24,000, then how long will it take for the car to be worth half of its value?

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