Final answer:
It took 56 minutes for the bacteria to fill a quarter of the 10-liter container. This calculation is based on understanding that if bacteria double every 2 minutes and fill the container at 58 minutes, then they would fill a quarter of it at 56 minutes due to exponential growth.
Step-by-step explanation:
The correct answer is that it took 56 minutes for the bacteria to fill a quarter of the 10-liter container. Knowing that the bacteria double every 2 minutes and that the container is full after 58 minutes, we can determine how long it would take to fill a quarter of the container by working backwards from full capacity.
It's important to recognize the exponential growth pattern here. At 58 minutes, the container is full, so at 56 minutes, it would be half full because the bacteria double every 2 minutes. At 54 minutes, the container would be a quarter full because, again, after two minutes (at 56 minutes), it would double to become half full, and at 58 minutes, it would double again to become completely full. Hence, it took 56 minutes to reach a quarter capacity.
This problem illustrates the nature of exponential growth, where in the final moments of such a process, growth occurs extremely rapidly compared to the earlier stages. This concept is relevant across various scientific disciplines, including biology and ecology.