SOLUTION: Jacques bought a new car for $15000. Each year, the value of the car depreciates to 70% of its value the previous year. In how many years will the car be worth only $500?

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: Jacques bought a new car for $15000. Each year, the value of the car depreciates to 70% of its value the previous year. In how many years will the car be worth only $500?       Log On

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Question 390342: Jacques bought a new car for $15000. Each year, the value of the car depreciates to 70% of its value the previous year. In how many years will the car be worth only $500?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
If the 1st year was x
after 1 year .7x
after 2 years .7%2A.7x
after 3 years .7%2A.7%2A.7x
The general formula would be:
.7%5En+%2A+x = dollars of value after n years
.7%5En+%2A15000+=+500
.7%5En+=+500%2F15000
.7%5En+=+1%2F30
Take the log of both sides
n%2Alog%28.7%29+=+-log%2830%29
n+=+%28-log%2830%29%29%2Flog%28.7%29
n+=+%28-1.477%29%2F+%28-.1549%29+=+9.535
About 9 years, 6 months and 13 days