document.write( "Question 982141: a machine depreciates in value each year by 8% of its value at the beginning of the year. After how many years will its value first be less than half its original value? \n" ); document.write( "

Algebra.Com's Answer #603022 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+V+\"$ = it's original value
\n" ); document.write( "Let $\"+V%2F2+\"$ = it's final value
\n" ); document.write( "---------------------------
\n" ); document.write( "Let $\"+n+\"$ = number of years until
\n" ); document.write( " $\"+V+\"$ becomes $\"+V%2F2+\"$
\n" ); document.write( "--------------------------
\n" ); document.write( " $\"+V%2F2+=+V%2A%28+1+-+.08+%29%5En+\"$
\n" ); document.write( "Divide both sides by $\"+V+\"$
\n" ); document.write( " $\"+1%2F2+=+%28+1+-+.08+%29%5En+\"$
\n" ); document.write( " $\"+1%2F2+=+.92%5En+\"$
\n" ); document.write( " $\"+log%28+.5+%29+=+n%2Alog%28+.92+%29+\"$
\n" ); document.write( " $\"+n+=+log%28+.5+%29+%2F+log%28+.92+%29+\"$
\n" ); document.write( " $\"+n+=+.30103+%2F+.03621+\"$
\n" ); document.write( " $\"+n+=+8.3134+\"$
\n" ); document.write( "At the end of the 8th year, the value will
\n" ); document.write( "be less than 1/2 of it's original value
\n" ); document.write( "----------------------------------
\n" ); document.write( "check:
\n" ); document.write( " $\"+1%2F2+=+.92%5En+\"$
\n" ); document.write( " $\"+.5+=+.92%5E8.3134+\"$
\n" ); document.write( " $\"+.5+=+.49998+\"$
\n" ); document.write( "close enough\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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