A car is purchased for 16,000Each year it loses 25% of its value. After how many years will the car be worth $4100 or less?

Answer 1

after one year it's worth 16,000(1-.25) = $12,000

after two years it's worth 12,000(1-.25) = $9,000

after three years it's worth 9,000(.75) = $6750

after four years it's worth 6750(.75) = $5062.50

after five years it's worth 5062.5(.75) = $3796.88

after n years it's worth 16,000(.75)^t where t = number of years

It's worth $4100 after between 4 and 5years

4100 = 16000(.75)^t

solve for t

(.75)^t = 4100/16000 =41/160

.75^t = .25625

.75^4.733 = .25625

t=4.733 years

after about 4 years and 9 months, the car's value is $4100