A new car is purchased for 22900 dollars. The value of the car depreciates at 6% per year. To the nearest year, how long will it be until the value of the car is 15700 dollars?<…

Question

asked Jul 23, 2021 138k views

2 Answers

Chris Gong · Answer 1 · 2021-07-29T04:07:28+0000

Answer:6.1 years

Explanation:

Given

Current worth
$C=\$ \ 22900$

rate of depreciates is
$D=6\ \%$ per year

worth after T years is
$W=\$ \ 15700$

Worth after T years

W=C(1-(D)/(100))^T

15700=22900(1-(D)/(100))^T

0.3776=0.94^T

Taking log on both sides

$T=(\ln 0.6855)/(\ln 0.94)$

$T=6.10\ years$

So it takes 6.1 years to depreciate