document.write( "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
\n" ); document.write( "$5,000? \n" ); document.write( "

Algebra.Com's Answer #715638 by josmiceli(19441) $\"\"$ $\"About$

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$\"+V%28t%29+=+57000%2Ae%5E%28-.2t%29+%2B+3500+\"$
\n" ); document.write( " $\"+5000+=+57000%2Ae%5E%28-.2t%29+%2B+3500+\"$
\n" ); document.write( " $\"+57000%2Ae%5E%28-.2t%29+=+1500+\"$
\n" ); document.write( " $\"+e%5E%28-.2t%29+=+.0263158+\"$
\n" ); document.write( "Take the natural log of both sides
\n" ); document.write( " $\"+-.2t+=+-3.63759+\"$
\n" ); document.write( " $\"+t+=+18.18793+\"$
\n" ); document.write( "and
\n" ); document.write( " $\"+.18793%2A12+=+2.255+\"$
\n" ); document.write( "It will take 18 yrs and 2 mos to
\n" ); document.write( "depreciate to $5,000
\n" ); document.write( "-----------------------------
\n" ); document.write( "check:
\n" ); document.write( " $\"+57000%2Ae%5E%28-.2t%29+=+1500+\"$
\n" ); document.write( " $\"+57000%2Ae%5E%28-3.63759%29+=+1500+\"$
\n" ); document.write( " $\"+57000%2A.0263157+=+1500+\"$
\n" ); document.write( " $\"+1499.9942+=+1500+\"$
\n" ); document.write( "close enough \n" ); document.write( "

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