Suppose that a bacterium lives in a test tube and the bacteria population doubles every minute, so that at the end of one minute there are two, at the end of two minutes there are four, and so on. Suppose also that at the end of fifteen minutes, the food supply runs out.

1. How many bacteria will be around at the end of 15 minutes?

2. How many bacteria will be around at the end of 14 minutes?

3. When will half of the food be used up?

4. What percentage of the food will be left at the end of 13 minutes?Do you think that, after 13 minutes, ‘‘Joe Average’’ bacterium would be easily persuaded that a food crisis was at hand?

5. Suppose, despite your answer to question 4, that at the beginning of the 13th minute the bacteria do get awake-up call. They begin a crash scientific program, putting the best bacteria minds to work on growing more food. Success! By the beginning of the 14th minute, the bacteria manage to quadruple the remaining food supply. How much time do they buy themselves?

6. Is there a difference between these bacteria and people that might give us some hope for our long-run survival? If so, is it likely to work through P,A, or T?