Jonas purchased a new car for $25,000. Each year the value of the car depreciates by 20% of its value the previous year. In how many years will the car be worth $5000?

Answer 1

25000(.8)^n = 5000
.8^n = .2
take log of both sides , and using log rules

n log.8 = log.2
n = log .2/log .8 = appr 7.2 years

Answer 2

This is actually a geometric series problem...which has the formula

An=(A1)(r)^(n-1)

so substitute the given

r=1-1/5 = 4/5
5000 = (25000)(4/5)^(n-1)
5000/25000 = (4/5)^(n-1)
1/5 = (4/5)^(n-1)

take ln on both sides

ln(1/5) = ln[(4/5)^(n-1)]
ln(1/5) = (n-1)ln(4/5)
n = [ln(1/5)/ln(4/5)]+1

n = 8.21 years