Final answer:
In 3 hours, a single prokaryotic cell with a 30-minute generation time will divide 6 times, resulting in a total of 64 cells on the petri dish.
Step-by-step explanation:
The number of prokaryotic cells present after 3 hours, given that the generation time is 30 minutes for one cell, can be calculated using the formula for exponential growth during binary fission. The number of times the cell will divide in 3 hours (which is 180 minutes) can be determined by dividing the total time by the generation time: 180 minutes / 30 minutes = 6 divisions. The population size after 3 hours will be 26 (because the population doubles with each division), which equals 64 cells.
Binary fission is a method of asexual reproduction employed by prokaryotes where one cell divides into two equal daughter cells. If a prokaryote such as Escherichia coli has a generation time of 30 minutes, it means that it will take 30 minutes for the bacterial population to double in size under optimal conditions. Over a duration of 3 hours, which is 180 minutes, the bacterium will have enough time to undergo this process of division 6 times (180 divided by 30), as the population doubles with each division cycle. Therefore, starting with a single bacterial cell, after the first 30 minutes, there will be 2 cells, then 4 cells after an hour, 8 cells after 1.5 hours, and so on until the 3-hour mark is reached. By using the formula 2n, where 'n' is the number of division cycles, we arrive at 26 = 64 cells after 3 hours, assuming an unimpeded growth without any environmental constraints such as nutrient depletion or waste accumulation that might inhibit growth or cause death.