Here are two problems I can't figure out.

Mclaughlin wrote:A certain culture of bacteria quadruples every hour. If a container with these bacteria was half full at 10:00 a.m., at what time was it one-eighth full?
(A) 9:00 a.m.
(B) 7:00 a.m.
(C) 6:00 a.m.
(D) 4:00 a.m.
(E) 2:00 a.m.

This problem is easily solved if you work it forwards, starting from the time the container was ⅛ full. Let’s start there:

1/8 x 4 = 1/2

So we see it took 1 hour to go from 1/8 full to 1/2 full. So at 9 am it was 1/8 full.

Alternate Solution:

Since the number of bacteria quadruple every hour, let’s go backwards in time from the point where the container was ½ full:

(½)/4 = (½)/(4/1) = (½) x (¼) = ⅛.

We see that one hour earlier, the container was ⅛ full of bacteria. This was at 9 am.

Answer: A