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The generation time G for a particular bacteria is the time it takes for the population to double. The bacteria increase in population is shown by the formula , where t is the time period of the population increase, a is the number of bacteria at the beginning of the time period, and P is the number of bacteria at the end of the time period. If the generation time for the bacteria is 6 hours, how long will it take 8 of these bacteria to multiply into a colony of 7681 bacteria? Round to the nearest hour.

 

the answers can be:

A 177

B 76

C 4

D 85

math
 Aug 18, 2014

Best Answer 

 #1
avatar+129896 
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Filling what we know, we have

6 = t / (3.3log8 7681)    ....and, using the "change of base" rule, we can write

6 = t / [(3.3)log 7681/log8)     .......and multiplying both sides by the denominator on the right, we have

6(3.3)log7681/log8 = t ≈ 85 hrs (rounded)

 

 Aug 18, 2014

1+0 Answers

 #1
avatar+129896 
+10
Best Answer

 

Filling what we know, we have

6 = t / (3.3log8 7681)    ....and, using the "change of base" rule, we can write

6 = t / [(3.3)log 7681/log8)     .......and multiplying both sides by the denominator on the right, we have

6(3.3)log7681/log8 = t ≈ 85 hrs (rounded)

 

CPhill Aug 18, 2014

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