document.write( "Question 978768: A recently released collectible quarter, worth 25 cents now, is expected to increase in value by 8% per year. How much is the coin expected to be worth in 109 years? \n" ); document.write( "

Algebra.Com's Answer #600141 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
For now, let $\"+v+\"$ = the starting value of the coin
\n" ); document.write( "After 1 year:
\n" ); document.write( "Value = $\"+v+%2B+.08v+\"$
\n" ); document.write( "After 2 years:
\n" ); document.write( "Value = $\"+%28+v+%2B+.08v+%29+%2B+%28+v+%2B+.08+%29%2A.08+\"$
\n" ); document.write( "Value = $\"+%28+v+%2B+.08v+%29%2A%28+1+%2B+.08+%29+\"$
\n" ); document.write( "Value = $\"+v%2A%28+1+%2B+.08+%29%5E2+\"$
\n" ); document.write( "After 3 years:
\n" ); document.write( "Value = $\"+v%2A%28+1+%2B+.08+%29%5E3+\"$
\n" ); document.write( "After 109 years:
\n" ); document.write( "Value = $\"+.25%2A%28+1+%2B+.08+%29%5E109+\"$
\n" ); document.write( "Take the log of both sides
\n" ); document.write( " $\"+log%28+V+%29+=+log%28%28+1.08%5E109+%29%29+%2B+log%28%28+.25+%29%29+\"$
\n" ); document.write( " $\"+log%28+V+%29+=+109%2Alog%28%28+1.08+%29%29+%2B+log%28%28+.25+%29%29+\"$
\n" ); document.write( " $\"+log%28+V+%29+=+109%2A.03342+-+.60206+\"$
\n" ); document.write( " $\"+log%28+V+%29+=+3.6432+-+.60206+\"$
\n" ); document.write( " $\"+log%28+V+%29+=+3.04114+\"$
\n" ); document.write( " $\"+V+=++1099.36+\"$
\n" ); document.write( "The coin will be worth $1,099.36 in 109 years
\n" ); document.write( "check:
\n" ); document.write( "Value = $\"+.25%2A%28+1+%2B+.08+%29%5E109+\"$
\n" ); document.write( "Value = $\"+.25%2A1.08%5E109+\"$
\n" ); document.write( "Value = $\"+.25%2A4397.333+\"$
\n" ); document.write( "Value = $\"+1099.33+\"$
\n" ); document.write( "OK\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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