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.
(1 point)
Responses
95 hours
95 hours
132 hours
132 hours
2 hours
2 hours
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), where G is the generation time, t is the time period of population increase, a is the number of bacteria at the beginning of the time period (4 in this case), and p is the number of bacteria at the end of the time period (7525 in this case).
Plugging in the values, we have G = 4.5, a = 4, and p = 7525.
G = t/3.3log(a/p)
4.5 = t/3.3log(4/7525)
To solve for t, we can multiply both sides by 3.3log(4/7525):
4.5 * 3.3log(4/7525) = t
t ≈ 57.17
Rounding 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:
57 hours