Question 212782
Growth of bacteria. The bacteria Escherichia coli (E. coli) are commonly found in the human bladder. Suppose that 3000 of the bacteria are present at time t=0. Then t minutes later, the number of bacteria present is N(t) = 3000(2)^t/20. if 100,000 bacteria accumulate, a bladder infection can occur. If, at 11:00am, a patient's bladder contains 25,000 E. coli bacteria, at what time can infection occur?
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100,000 = 3000*2^(t/20)
2^(t/20) = 100/3
(t/20)ln2 = ln(100/3)
t = 20[ln(100/3)]/[ln(2)]
t = 101.18 minutes (time after time = 0 to reach 100,000)
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25000 = 3000*2^(t/2)
2^(t/2) = 25/3
t = 2[ln(25/3)/ln(2)]
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t = 6.18 minutes (time after time = 0 to reach 25000)
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Time from 25000 to 100000: 101.18-6.18 = 95 minutes
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95 minutes after 11:00 the time will be 12:35 PM
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Cheers,
Stan H.