SOLUTION: The value of a car halves in 3 years. Find its annual rate of depreciation or loss in value.

Algebra ->  Finance -> SOLUTION: The value of a car halves in 3 years. Find its annual rate of depreciation or loss in value.      Log On


   

Question 1005212: The value of a car halves in 3 years. Find its annual rate of depreciation or loss in value.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
let +a+ = the initial value of the car
Let +b+ = the fraction that the value
gets reduced by each year
-------------------------
After 1st year:
+a+-+b%2Aa+=+a%2A%28+1+-+b+%29+
After 2nd year:
+a%2A%28+1+-+b+%29+-+b%2A%28+a%2A%28+1+-+b+%29+%29+=+a%2A%28+1+-+b+%29%2A%28+1+-+b+%29+
--------------------------
The rule is:
Current value of car=
+a%2A%28+1+-+b+%29%5En+ after +n+ years
-------------------------------
You are given that:
+a%2F2+=+a%2A%28+1+-+b+%29%5E3+
Divide both sides by +a+
+1%2F2+=+%28+1+-+b+%29%5E3+
Take the log of both sides
+log%28+1%2F2+%29+=+3%2Alog%28%28+1+-+b+%29%29+
+-.301+=+3%2Alog%28%28+1+-+b+%29%29+
+log%28%28+1+-+b+%29%29+=+-.10034+
+1+-+b+=+10%5E%28-.10034%29+
+1+-+b+=+.7937+
+b+=+.2063+
The annual depreciation is 20.63%
Hope I got it -you might want to get
another opinion on this