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/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 95 hours
b 132 hours
c 2 hours
d 57 hours
To find the time it takes for 4 bacteria to multiply into a colony of 7525 bacteria, we can use the formula G=t/3.3log_a p.
Given:
Generation time (G) = 4.5 hours
a = 4 (number of bacteria at the beginning)
p = 7525 (number of bacteria at the end)
We need to find t, the time period of the population increase.
Using the formula G=t/3.3log_a p, we can solve for t:
4.5 = t/3.3log_4 7525
First, find the logarithm of 7525 with base 4:
log_4 7525 ≈ 5.1391
Now, we can solve for t:
4.5 = t/3.3(5.1391)
4.5 = t/(16.89103)
t = 4.5 * 16.89103
t ≈ 76.01065 hours
Rounding to the nearest hour, it will take approximately 76 hours for 4 bacteria to multiply into a colony of 7525 bacteria.
Therefore, the correct answer is not provided among the given options.