document.write( "Question 1181923: On a small island there were 32768 deer and only 128 wolves. Statistics gathered revealed that the wolf population doubled every 3 years and the deer population halved every 6 years. How many years did it take for the wolf population to overtake the deer population? Create an algebraic solution to the problem. \n" ); document.write( "

Algebra.Com's Answer #811887 by ikleyn(52797) $\"\"$ $\"About$

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\n" ); document.write( "On a small island there were 32768 deer and only 128 wolves. Statistics gathered revealed that
\n" ); document.write( "the wolf population doubled every 3 years and the deer population halved every 6 years.
\n" ); document.write( "How many years did it take for the wolf population to overtake the deer population?
\n" ); document.write( "Create an algebraic solution to the problem.
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document.write( "From the condition, we have \r\n" );
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document.write( "    D(t) = 32768*1/2)^(t/6)     (1)\r\n" );
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document.write( "for deer population and\r\n" );
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document.write( "    W(t) = 128*2^(t/3)          (2)\r\n" );
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document.write( "for wolves population.\r\n" );
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document.write( "To answer the question, we should solve this equation\r\n" );
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document.write( "    D(t) = W(t),   or  32768*(1/2)^(t/6) = 128*2^(t/3).    (3)\r\n" );
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document.write( "It implies\r\n" );
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document.write( "     = 2^(t/3) * 2^(t/6),\r\n" );
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document.write( "or\r\n" );
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document.write( "    256 = 2^(t/3 + t/6)\r\n" );
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document.write( "    2^8 = 2^(2t/6 + t/6)\r\n" );
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document.write( "    2^8 = 2^(3t/6) = 2^(t/2).\r\n" );
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document.write( "Hence,   = 8  and  t = 2*8 = 16  years.      ANSWER\r\n" );
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