document.write( "Question 130669: Two types of bacteria are grown in a lab and their populations studied. One population initially contained 320 spores and was found to triple in size every 12 days. The second population initially contained 800 spores and has a half-life of 8 days. After how many days will the two bacteria cultures have the same number of spores? \n" ); document.write( "

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Two types of bacteria are grown in a lab and their populations studied. One population initially contained 320 spores and was found to triple in size every 12 days. The second population initially contained 800 spores and has a half-life of 8 days. After how many days will the two bacteria cultures have the same number of spores?
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\n" ); document.write( "EQUATION:
\n" ); document.write( "320*3^(t/12) = 800*(1/2)^(t/8)
\n" ); document.write( "0.4*3^(t/12) = (1/2)^(t/8)
\n" ); document.write( "Take the log of both sides to get:
\n" ); document.write( "log0.4 + (t/12)log3 = (t/8)log(1/2)
\n" ); document.write( "Multiply thru by 24 to get:
\n" ); document.write( "24log0.4 + 2tlog3 = 3tlog(0.5)
\n" ); document.write( "-9.55 = t(3log(0.5)-log(3))
\n" ); document.write( "-9.55 = t(-1.380211)
\n" ); document.write( "t = 6.9192 days
\n" ); document.write( "==================
\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H. \n" ); document.write( "

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