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) 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 need to use the formula G = t/3.3log(a/p), where G is the generation time, t is the time period, a is the number of bacteria at the beginning, and p is the number of bacteria at the end.
We are given that G = 4.5 hours, a = 4 bacteria, and p = 7525 bacteria. Plugging in these values into the formula, we get:
4.5 = t/3.3log(4/7525)
To solve for t, we can multiply both sides of the equation by 3.3log(4/7525):
4.5 * 3.3log(4/7525) = t
Using a calculator to evaluate 3.3log(4/7525), we get approximately -36.42.
Therefore, t = 4.5 * -36.42, which is approximately -163.89.
Since time cannot be negative, we must round -163.89 to the nearest hour, which is -164.
Therefore, it will take approximately 164 hours for 4 bacteria to multiply into a colony of 7525 bacteria.
The closest option is D) 57 hours.