document.write( "Question 128802: Michael purchases a rare coin for $100 that will double in value every 9 years. His friend John purchases a rare book for $75 that will double in value every 6 years. If both purchases were made at the same time, in how many years will they be of equal value??? Please HELP me :) \n" ); document.write( "

Algebra.Com's Answer #94213 by stanbon(75887) $\"\"$ $\"About$

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Michael purchases a rare coin for $100 that will double in value every 9 years. His friend John purchases a rare book for $75 that will double in value every 6 years. If both purchases were made at the same time, in how many years will they be of equal value???
\n" ); document.write( "--------------------------
\n" ); document.write( "Coin DATA:
\n" ); document.write( "Value = 100*(2^t/9)
\n" ); document.write( "---------------------
\n" ); document.write( "Book DATA:
\n" ); document.write( "Value = 75*(2^t/6)
\n" ); document.write( "--------------------------
\n" ); document.write( "EQUATION:
\n" ); document.write( "value = value
\n" ); document.write( "100(2^(t/9)) = 75(2^(t/6))
\n" ); document.write( "2^(t/6-t/9) = 100/75
\n" ); document.write( "2^(3t/54) = 4/3
\n" ); document.write( "2^(t/18) = 4/3
\n" ); document.write( "Take the log of both sides to get:
\n" ); document.write( "(t/18)log(2) = log(4/3)
\n" ); document.write( "t/18 = 0.4150
\n" ); document.write( "t = 7.47 years
\n" ); document.write( "===================
\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H. \n" ); document.write( "

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