Answer :
To determine the fraction of the bottle that was full at 11:20 a.m., let's analyze the situation in a step-by-step manner using the information given: the bacteria doubles every five minutes.
1. Understand the doubling pattern: If the bacteria doubles every five minutes, this means that five minutes before the bottle is full, it would be half full.
2. Establish the known point: Let’s assume the bottle is completely full at 11:25 a.m.
3. Step back in time: To find out how full the bottle was at 11:20 a.m., we need to consider the time difference in terms of bacterial growth:
- From 11:25 a.m. to 11:20 a.m. is a 5-minute interval.
- Since the bacteria doubles every five minutes, it means that going backward by five minutes, the amount of bacteria must halve.
4. Apply the pattern:
- At 11:25 a.m., the bottle is full (which we can consider as 1 whole bottle, or a fraction of 1/1).
- Therefore, five minutes earlier (at 11:20 a.m.), the bottle would be half as full as it is at 11:25 a.m.
5. Determine the solution:
- If the bottle is full at 11:25 a.m., then at 11:20 a.m., it would be half full.
- Thus, the fraction of the bottle that was full at 11:20 a.m. is [tex]\( \frac{1}{2} \)[/tex].
Therefore, the fraction of the bottle that was full at 11:20 a.m. is [tex]\( \frac{1}{2} \)[/tex].
1. Understand the doubling pattern: If the bacteria doubles every five minutes, this means that five minutes before the bottle is full, it would be half full.
2. Establish the known point: Let’s assume the bottle is completely full at 11:25 a.m.
3. Step back in time: To find out how full the bottle was at 11:20 a.m., we need to consider the time difference in terms of bacterial growth:
- From 11:25 a.m. to 11:20 a.m. is a 5-minute interval.
- Since the bacteria doubles every five minutes, it means that going backward by five minutes, the amount of bacteria must halve.
4. Apply the pattern:
- At 11:25 a.m., the bottle is full (which we can consider as 1 whole bottle, or a fraction of 1/1).
- Therefore, five minutes earlier (at 11:20 a.m.), the bottle would be half as full as it is at 11:25 a.m.
5. Determine the solution:
- If the bottle is full at 11:25 a.m., then at 11:20 a.m., it would be half full.
- Thus, the fraction of the bottle that was full at 11:20 a.m. is [tex]\( \frac{1}{2} \)[/tex].
Therefore, the fraction of the bottle that was full at 11:20 a.m. is [tex]\( \frac{1}{2} \)[/tex].
