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: Assume bottle full at 11:40

Let full bottle = $1$ at 11:40 a.m.

Step2: Work backward to 11:35

Bacteria doubles every 5 mins, so reverse: divide by 2.
$1 \div 2 = \frac{1}{2}$

Step3: Work backward to 11:30

Divide previous value by 2.
$\frac{1}{2} \div 2 = \frac{1}{4}$

Step4: Work backward to 11:25

Divide previous value by 2.
$\frac{1}{4} \div 2 = \frac{1}{8}$

Step5: Work backward to 11:20

Divide previous value by 2.
$\frac{1}{8} \div 2 = \frac{1}{16}$

Answer:

$\frac{1}{16}$