document.write( "Question 184656: the number of bacteria in a culture increased sixfold in 10 hours. Assuming natural growth, how long did it take their number to double? \n" ); document.write( "
Algebra.Com's Answer #138598 by Edwin McCravy(20059)\"\" \"About 
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the number of bacteria in a culture increased sixfold in 10 hours. Assuming natural growth, how long did it take their number to double?
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document.write( "Your textbook and teacher may be using different letters from the\r\n" );
document.write( "ones I use, if so you can change the letters to yours.\r\n" );
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document.write( "\"P+=+P%5B0%5De%5E%28rt%29\"\r\n" );
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document.write( "\"P\" has gone from \"P%5B0%5D\" to \"6%2AP%5B0%5D\" while t increased to \"10\".  \r\n" );
document.write( "So we substitute \"6%2AP%5B0%5D\" for \"P\" and \"10\" for \"t\":\r\n" );
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document.write( "\"6%2AP%5B0%5D+=+P%5B0%5De%5E%28r%2A10%29\"\r\n" );
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document.write( "Divide both sides by \"P%5B0%5D\"\r\n" );
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document.write( "\"6+=+e%5E%2810r%29\"\r\n" );
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document.write( "Change to natural log form:\r\n" );
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document.write( "\"10r+=+ln%286%29\"\r\n" );
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document.write( "\"r+=+ln%286%29%2F10\"\r\n" );
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document.write( "\"r+=+.1791759469\"\r\n" );
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document.write( "So we take the original formula\r\n" );
document.write( "and substitute \".1791759469\"\r\n" );
document.write( "for r.\r\n" );
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document.write( "\"P+=+P%5B0%5De%5E%28rt%29\"\r\n" );
document.write( "\"P+=+P%5B0%5De%5E%28.1791759469t%29\"\r\n" );
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document.write( "Now we want to find what \"t\" is when \"P=2%2AP%5B0%5D\"\r\n" );
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document.write( "\"2%2AP%5B0%5D+=+P%5B0%5De%5E%28.1791759469t%29\"\r\n" );
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document.write( "\"2%2AP%5B0%5D+=+P%5B0%5De%5E%28.1791759469t%29\"\r\n" );
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document.write( "Divide both sides by \"P%5B0%5D\"\r\n" );
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document.write( "\"2+=+e%5E%28.1791759469t%29\"\r\n" );
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document.write( "Change to natural log form:\r\n" );
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document.write( "\".1791759469t+=+ln%282%29\"\r\n" );
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document.write( "\"t+=+ln%282%29%2F.1791759469\"\r\n" );
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document.write( "\"t+=+3.868528072hours\"\r\n" );
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document.write( "Edwin
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