SOLUTION: 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?

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: 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?      Log On

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Question 959561: 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 by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
After +n+ years, the car is worth
+25000%2A%28+1+-+.2+%29%5En+
given:
+5000+=+25000%2A.8%5En+
+1%2F5+=+.8%5En+
+.2+=+.8%5En+
Take the log of both sidesd
+n%2Alog%28+.8+%29+=+log%28+.2+%29+
+n+=+log%28+.2+%29+%2F+log%28+.8+%29+
+n+=+-.69897+%2F+-.0961+
+n+=+7.273+
In 7 years the car will be worth $5,000
check:
+.2+=+.8%5En+
+.2+=+.8%5E7.273+
+.2+=+.197+
close enough I think