SOLUTION: Suppose that an automobile loses 1/5 of its value each year, that is at the end of a given year, the value is 4/5 of the value at the begging of that year. If a car cost 19000 new,

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Question 517098: Suppose that an automobile loses 1/5 of its value each year, that is at the end of a given year, the value is 4/5 of the value at the begging of that year. If a car cost 19000 new, what is the value at the end of five years?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +n+=+19000+, the cost when new
Let +v+ = the current value
At end of 1st year:
+v+=+%284%2F5%29%2An+
At end of 2nd year:
+v+=+%284%2F5%29%2A%284%2F5%29%2An+
At end of 3rd year:
+v+=+%284%2F5%29%2A%284%2F5%29%2A%284%2F5%29%2An+
At end of 4th year:
+v+=+%284%2F5%29%2A%284%2F5%29%2A%284%2F5%29%2A%284%2F5%29%2An+
At the end of the 5th year:
+v+=+%284%2F5%29%2A%284%2F5%29%2A%284%2F5%29%2A%284%2F5%29%2A%284%2F5%29%2An+
-------------
This is the same as +%284%2F5%29%5E5+%2A+n+
+%284%2F5%29%5E5+=+1024%2F3125+
+%284%2F5%29%5E5+=+.32768+
+.32768%2A19000+=+6225.92+
The value after 5 years is $6,225.92