Question

use the fact that the bacteria is doubling every five minutes. what fraction of the bottle was full at 11:20 a.m.?

Explanation:

Step1: Analyze time - interval

The time from 11:20 a.m. to 11:40 a.m. is 20 minutes. Since the bacteria doubles every 5 minutes, the number of 5 - minute intervals is $\frac{20}{5}=4$ intervals.

Step2: Work backwards

Let the amount of bacteria at 11:40 a.m. be 1 (full - bottle). Since the bacteria doubles every 5 minutes, going back one 5 - minute interval, the amount of bacteria is halved.
If we go back 4 five - minute intervals from 11:40 a.m. to 11:20 a.m., we divide by 2 four times.
The amount of bacteria at 11:20 a.m. is $\frac{1}{2^4}=\frac{1}{16}$.

Answer:

$\frac{1}{16}$