Imagine that you once again have a species of bacteria that asexually divides, but this time it divides once a minute. so if you start with one bacterium at time 0, then after 1 minute you have 2 bacteria; after 2 minutes you have 4, etc. imagine that you place one of these bacteria into a bottle at 11: 00 p. m. and that at midnight (one hour later) that bottle is completely full.

1. at what time will the bottle be exactly half-full? how did you figure this out?

2. at what time might an intelligent, environmentally conscious bacterium in this bottle realize that its species was running out of space? why?