document.write( "Question 1127693: find the formula for an exponential function that passes through the two points given.
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Algebra.Com's Answer #744183 by ikleyn(52790)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "            Below find my solution for case a).\r
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\n" ); document.write( "\n" ); document.write( "find the formula for an exponential function that passes through the two points given.
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document.write( "General exponential function formula\r\n" );
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document.write( "    y = \"ab%5Ex\".        (1)\r\n" );
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document.write( "At  x= -1,  y= \"1%2F2\"  formula (1) becomes   \"1%2F2\" = \"a%2Ab%5E%28-1%29\"    (2).\r\n" );
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document.write( "At  x= 4,  y= 512  formula (1) becomes   512 = \"a%2Ab%5E4\"    (3).\r\n" );
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document.write( "Divide  (3)  by (2).  You will get\r\n" );
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document.write( "    \"512%2F%28%281%2F2%29%29\" = \"b%5E4%2Fb%5E%28-1%29\",   or, equivalently,\r\n" );
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document.write( "    1024 = \"b%5E5\",\r\n" );
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document.write( "    \"4%5E5\" = \"b%5E5\".\r\n" );
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document.write( "It implies  b = 4,  so half of the problem is just solved.\r\n" );
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document.write( "Now substitute the found value b= 4 into equation (3). You will get\r\n" );
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document.write( "    512 = \"a%2A4%5E4\",  \r\n" );
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document.write( "which implies  a = \"512%2F4%5E4\" = \"512%2F256\" = 2.\r\n" );
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document.write( "Answer.  The function is  y = \"2%2A4%5Ex\".\r\n" );
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