SOLUTION: 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 popu

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?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
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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EQUATION:
320*3^(t/12) = 800*(1/2)^(t/8)
0.4*3^(t/12) = (1/2)^(t/8)
Take the log of both sides to get:
log0.4 + (t/12)log3 = (t/8)log(1/2)
Multiply thru by 24 to get:
24log0.4 + 2tlog3 = 3tlog(0.5)
-9.55 = t(3log(0.5)-log(3))
-9.55 = t(-1.380211)
t = 6.9192 days
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Cheers,
Stan H.
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