The generation time G for a particular bacterium is the time it takes for the population to double. The bacteria increase in population is shown by the formula G = t over 3.3log a p, 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 4.5 hours, how long will it take 4 of these bacteria to multiply into a colony of 7525 bacteria? Round to the nearest hour.

Question

A. 96 hours

B. 132 hours

C. 2 hours

D. 57 hours

Answer 1

First, we need to identify the values given in the problem:

- Generation time (G) = 4.5 hours
- Number of bacteria at the beginning (a) = 4
- Number of bacteria at the end (P) = 7525

Now we can plug these values into the formula G = t / 3.3log a P and solve for t:

4.5 = t / (3.3log4 7525)
4.5 = t / (3.3 x 2log 7525)
4.5 = t / (3.3 x 2 x 3.877)
4.5 = t / 25.5
t = 4.5 x 25.5
t = 114.75

Therefore, it will take approximately 114.75 hours for 4 bacteria to multiply into a colony of 7525 bacteria. Rounded to the nearest hour, the answer is 115 hours.

Therefore, the closest option is:

B. 132 hours

Answer 2

Stupid robot, the answer is actually 96 hours. Learn facts before you say stuff little goof.

Answer 3

I apologize for the error in my response. Let's recalculate:

Given:
- Generation time (G) = 4.5 hours
- Number of bacteria at the beginning (a) = 4
- Number of bacteria at the end (P) = 7525

We will use the formula G = t / 3.3logₐP:

4.5 = t / (3.3log₄7525)
4.5 = t / (3.3 x 3.877)
4.5 = t / 12.77
t = 4.5 x 12.77
t ≈ 57.47 hours

Rounded to the nearest hour, it will take approximately 57 hours for 4 bacteria to multiply into a colony of 7525 bacteria.

Therefore, the correct answer is:

D. 57 hours

Answer 4

🤡

Answer 5

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