Final answer:
The jar would have been half full at 9:58, which is two minutes before it was completely full at 10:00. This illustrates the characteristic of exponential growth where most of the growth occurs in the final periods before reaching capacity. The correct option is approximately option D.
Step-by-step explanation:
The question deals with understanding the concept of exponential growth, specifically relating to a population of bacteria doubling over time. If a bacteria population doubles every two minutes and the jar is full at 10:00, to find out when the jar was half full, we need to take into account that exponential growth is a process where quantities grow by a constant proportion in each unit of time.
So, in this case, if the jar is full at 10:00, it means that right before it was full, it must have been half full. As the bacteria doubles every two minutes, this would be one doubling time before the jar became completely full.
Thus, if the population fills the jar at 10:00, it must have been half full at 9:58. This result aligns with our understanding of exponential growth, as the jar's population would look nearly empty for most of the preceding time, with most of the growth happening in the final intervals.
For instance, as per Figure 1.1 in the reference material, the jar would look almost empty until the last few doubling times, demonstrating the dramatic nature of exponential growth towards the end of the cycle.