Question! If you put a bacteria in a beaker that doubles itself every minute at 11 and it's full at 12 at what time is it half full
12:00 --- full
11:59 --- half-full <------
11:58 --- 1/4 full
To find out at what time the beaker is half full, we need to work backward from when it is full at 12 o'clock.
Given that the bacteria doubles every minute starting from 11 o'clock, we can represent the number of bacteria at each minute as follows:
- At 11 o'clock, there is 1 bacterium.
- At 11:01, it doubles to 2 bacteria.
- At 11:02, it doubles again to 4 bacteria.
- At 11:03, it doubles to 8 bacteria.
- And so on...
We can see that the number of bacteria doubles every minute until 12 o'clock. So, working backward from 12 o'clock, we can determine when the beaker would be half full.
- At 11:59, there are 2^59 bacteria (as we know it doubles every minute).
- At 11:58, there are half as many as at 11:59, so there would be 2^58 bacteria.
Therefore, the beaker would be half full at 11:58.