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.
96 hours
132 hours
2 hours
57 hours
To find out how long it will take for 4 bacteria to multiply into a colony of 7525 bacteria, we can use the generation time formula.
G = t / 3.3log(ap)
Given that the generation time G is 4.5 hours, a = 4, and P = 7525, we can plug in these values to find t:
4.5 = t / 3.3log(4(7525))
4.5 = t / 3.3log(30100)
4.5 = t / 3.3(4.4799)
4.5 = t / 14.7687
t = 4.5 * 14.7687
t = 66.45915 hours
Rounded to the nearest hour, it will take approximately 66 hours for 4 bacteria to multiply into a colony of 7525 bacteria.