A number of bacteria are placed in a glass. One second later each bacterium divides in two, the next second each of the resulting bacteria divides in two again, etc. After exactly one minute, the glass is full. When was the glass half full?

obviously at the 59 second mark.

At this point the glass is half-full
They all double to make the glass full in the next second

Assume his small imagine has 1 parental cell; Salmonella reproduces every 30 minutes. How many bacteria after 12 hours

To solve this problem, let's work backwards from when the glass is full after 1 minute.

In the last second, the glass had a certain number of bacteria, and during the previous second, each of those bacteria divided into two. So, the total number of bacteria in the glass 1 second before it was full was half the number that filled it.

Similarly, the glass was also half full 2 seconds before it was full because each bacterium divides into two every second.

Using this pattern, for each second that goes by, the glass is halved. Therefore, the glass was half full 30 seconds before it was full.

So, the glass was half full at 30 seconds.

To determine when the glass was half full, we need to understand the rate at which the number of bacteria doubles over time.

In this scenario, we have a doubling of bacteria every second. This means that the number of bacteria in the glass is increasing exponentially.

After one second, each bacterium divides in two, so the number of bacteria doubles. So, if we start with 1 bacterium, after 1 second, we will have 2 bacteria.

After another second, each of the 2 bacteria divide in two, resulting in 4 bacteria.

If we continue this doubling process for 60 seconds, we will find that the glass is full at the end of one minute.

To find when the glass was half full, we need to work backward. If the glass is full at 60 seconds, then we need to determine when there were half as many bacteria.

Since the doubling is exponential, we can estimate that the glass was half full one second before the glass became full. So, the glass was half full at 59 seconds.

Therefore, the glass was half full just one second before it became full at 59 seconds.