SOLUTION: 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 eve

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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.
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
Exponential growth is given by N+=+N%5B0%5De%5E%28kt%29+
For strain 1 we have 320+=+80e%5E%282k%29+
4+=+e%5E%282k%29
ln%284%29+=+2k
1.386+=+2k
0.693+=+k
The function for strain 1 is N+=+80e%5E%280.693t%29
Strain 2 is : 1280+=+640e%5E%28k5%29
2+=+e%5E%28k5%29
ln%282%29+=+k5
0.693+=+k5+
0.1386+=+k+

The function for strain 2 is N+=+640e%5E%280.1386t%29
At what time are they equal?
80e%5E%280.693t%29+=+640e%5E%280.1386t%29+
e%5E%280.693t%29+=+8e%5E%280.1386t%29
e%5E%280.693t%29%2Fe%5E%280.1386t%29++=+8
e%5E%280.5514t%29=+8
0.5514t=+ln%288%29
0.5514t=+2.079
3.77+=+t
Check your answer.