Final answer:
The jar is half full at 11:59 PM, one minute before midnight. You find this by working backwards from the full jar at midnight, considering the doubling time of one minute.
Step-by-step explanation:
The question you're asking involves exponential growth, specifically in regards to a scenario where bacteria are filling a jar. If the doubling time is one minute and the jar is full at midnight, to determine when the jar is half full, you simply go back one doubling period. In this case, since the doubling period is every minute, if the jar is full at midnight (12:00 AM), it would be half full at 11:59 PM.
The process involves working backwards from the endpoint. This type of problem is a classic demonstration of exponential growth and highlights how quickly growth can happen, especially towards the 'end' (full capacity of the jar), which is why it appears that most of the growth happens in the last moments.