SOLUTION: please solve help me solve this word problem: Lucy bought a car for $25,000. The value of the car depreciates by about 13% each year. when will the value of the car be $10,000 ?

Question 570809: please solve help me solve this word problem: Lucy bought a car for $25,000. The value of the car depreciates by about 13% each year. when will the value of the car be $10,000 ?
please help me. and please show me the work to get the answer because i have no idea how to solve this problem.
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Suppose for now the car starts out being worth
Let the yearly depreciation = ( .13, actually )
At end of 1st yr it is worth

At end of 2nd yr

At end of 3rd yr

------------------------
You can see the progression here
In your problem, and

I can say

where is the number of yrs car is owned

and
So, after 6 yrs ( 6 yrs and 7 months ),
the car is worth $10,000
---------------------------
I can check this

close enough
The key to understanding this problem is to see
that each years depreciation is on last year's
DEPRECIATED value. Hope this helps.

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