Question

analyzing doubling time
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: Define full bottle time

Let the bottle be full (fraction = $1$) at 11:20 a.m.

Step2: Work backward for 11:25 a.m.

Bacteria double every 5 minutes, so reverse: divide by 2.
$\frac{1}{2} \div 2 = \frac{1}{4}$

Step3: Work backward for 11:30 a.m.

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

Step4: Work backward for 11:35 a.m.

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

Step5: Work backward for 11:40 a.m.

Divide previous fraction by 2.
$\frac{1}{16} \div 2 = \frac{1}{32}$

Answer:

• 11:25 a.m.: $\frac{1}{4}$
• 11:30 a.m.: $\frac{1}{8}$
• 11:35 a.m.: $\frac{1}{16}$
• 11:40 a.m.: $\frac{1}{32}$