Final answer:
The generation time for a bacterium is the time it takes for the population to double. In the first scenario, it's 24 minutes per generation, and in the second scenario, it is approximately 30 minutes per generation.
Step-by-step explanation:
The generation time for a bacterium is the amount of time it takes for the bacterial population to double. To calculate the generation time for the first scenario, where a culture produces 5 generations in two hours, we divide the total time by the number of generations: 2 hours / 5 generations = 0.4 hours per generation, or 24 minutes per generation.
For the second scenario, involving an increase from 100 to 100,000,000 bacteria in 15 hours, we determine the number of generations by using the formula for exponential growth: N = N0 × 2g, where N is the final population size, N0 is the initial population size, and g is the number of generations. After rearranging to solve for g and substituting the given values (100,000,000 = 100 × 2g), we can determine g. We then divide the total time by the number of generations to find the generation time, which turns out to be about 30 minutes per generation.