Let's solve the problem step-by-step using the information provided.
We know that:
1. The bacteria in the bottle doubles every 5 minutes.
2. The bottle was fully filled with bacteria at 11:20 a.m.
To find out what fraction of the bottle was full at 11:15 a.m., we need to consider the doubling nature of the bacteria.
Here's the systematic thought process:
1. The bacteria population doubles every 5 minutes. This means if the bottle is fully filled at a specific time, it would have been half full 5 minutes earlier.
2. At 11:20 a.m., the bottle is fully filled, i.e., at its maximum capacity.
3. To determine the fraction of the bottle that was full 5 minutes before 11:20 a.m., we note that at 11:15 a.m., the bottle must have been half-full. This is because in the next 5 minutes (from 11:15 a.m. to 11:20 a.m.), the quantity of bacteria would double, filling the entire bottle by 11:20 a.m.
Through logical deduction:
- If the bottle is fully filled at 11:20 a.m., it must have been half-filled at 11:15 a.m. due to the doubling nature of the bacteria population.
Thus, the fraction of the bottle that was full at 11:15 a.m. is:
[tex]\[
\frac{1}{2}
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{\frac{1}{2}}
\][/tex]
