SOLUTION: The value V of a stand-by generator after t years of depreciation is given by the formula V(t) =57000e^−0.2t + 3500. Approximately how many years will it take for the value t

Algebra ->  Matrices-and-determiminant -> SOLUTION: The value V of a stand-by generator after t years of depreciation is given by the formula V(t) =57000e^−0.2t + 3500. Approximately how many years will it take for the value t      Log On


   



Question 1101063: The value V of a stand-by generator after t years of depreciation is given by the formula V(t) =57000e^−0.2t + 3500. Approximately how many years will it take for the value to depreciate to
$5,000?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+V%28t%29+=+57000%2Ae%5E%28-.2t%29+%2B+3500+
+5000+=+57000%2Ae%5E%28-.2t%29+%2B+3500+
+57000%2Ae%5E%28-.2t%29+=+1500+
+e%5E%28-.2t%29+=+.0263158+
Take the natural log of both sides
+-.2t+=+-3.63759+
+t+=+18.18793+
and
+.18793%2A12+=+2.255+
It will take 18 yrs and 2 mos to
depreciate to $5,000
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check:
+57000%2Ae%5E%28-.2t%29+=+1500+
+57000%2Ae%5E%28-3.63759%29+=+1500+
+57000%2A.0263157+=+1500+
+1499.9942+=+1500+
close enough