Final answer:
Bacteria can double in number quickly, as fast as every 20 minutes for E. coli in the best conditions. Exponential growth calculations show how rapidly bacterial populations can increase, making hypothetical scenarios like the bacteria jar example unrealistic when doubling occurs every 10 or even 30 minutes.
Step-by-step explanation:
Under favorable conditions, the time it takes for bacteria to double in population, known as the doubling time, can be as short as 20 minutes. However, doubling times can vary significantly depending on the bacterial species and environmental conditions. For a common bacterium like Escherichia coli, the doubling time can be 20 minutes in optimal laboratory conditions, while other bacteria may take much longer. For instance, Mycobacterium tuberculosis has a doubling time of 15 to 20 hours.
In the context of exponential growth and a hypothetical jar experiment where bacteria double every 10 minutes, calculations reveal that starting with a single bacterium, after 24 hours, the population would exceed 10¹⁶ bacteria, making the experimental setup unrealistic. Moreover, if the doubling time was every minute, the jar would be half full just one minute before midnight. If we increase the doubling time to a more realistic 30 minutes, we would need to calculate the starting amount so that after 24 hours, the jar holding 10¹⁶ bacteria would reach full capacity.
Understanding exponential growth also helps to predict population sizes at various intervals. For example, with a doubling time of 30 minutes, a starting population of 1 × 10⁵ cells would result in 8000 bacteria after three hours, showcasing the increasing rate of exponential growth.