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.
A. 96 hours
B. 132 hours
C. 2 hours
D. 57 hours
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
Stupid robot, the answer is actually 96 hours. Learn facts before you say stuff little goof.
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