document.write( "Question 135306: Michael is growing two strains of yeast in the labratory. Strain A originally had 80 cells and is known to quadruple every 2 hours. Strain B initially had 640 cells and doubles every 5 hours. When will Michael observe the same number of cells in the two yeast cultures. \n" ); document.write( "

Algebra.Com's Answer #99134 by vleith(2983) $\"\"$ $\"About$

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Exponential growth is given by $\"N+=+N%5B0%5De%5E%28kt%29+\"$ \r
\n" ); document.write( "\n" ); document.write( "For strain 1 we have $\"320+=+80e%5E%282k%29+\"$
\n" ); document.write( " $\"4+=+e%5E%282k%29\"$
\n" ); document.write( " $\"ln%284%29+=+2k\"$
\n" ); document.write( " $\"1.386+=+2k\"$
\n" ); document.write( " $\"0.693+=+k\"$ \r
\n" ); document.write( "\n" ); document.write( "The function for strain 1 is $\"N+=+80e%5E%280.693t%29\"$ \r
\n" ); document.write( "\n" ); document.write( "Strain 2 is : $\"1280+=+640e%5E%28k5%29\"$
\n" ); document.write( " $\"2+=+e%5E%28k5%29\"$
\n" ); document.write( " $\"ln%282%29+=+k5\"$
\n" ); document.write( " $\"0.693+=+k5+\"$
\n" ); document.write( " $\"0.1386+=+k+\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The function for strain 2 is $\"N+=+640e%5E%280.1386t%29\"$ \r
\n" ); document.write( "\n" ); document.write( "At what time are they equal?
\n" ); document.write( " $\"80e%5E%280.693t%29+=+640e%5E%280.1386t%29+\"$
\n" ); document.write( " $\"e%5E%280.693t%29+=+8e%5E%280.1386t%29\"$
\n" ); document.write( " $\"e%5E%280.693t%29%2Fe%5E%280.1386t%29++=+8\"$
\n" ); document.write( " $\"e%5E%280.5514t%29=+8\"$
\n" ); document.write( " $\"0.5514t=+ln%288%29\"$
\n" ); document.write( " $\"0.5514t=+2.079\"$
\n" ); document.write( " $\"3.77+=+t\"$ \r
\n" ); document.write( "\n" ); document.write( "Check your answer. \r
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