space resources have quadrupled, how long can their growth continue.

space resources have quadrupled, how long can their growth continue.
Doubling time is the time it takes a population to double at a constant rate of growth. Bacteria, for instance, multipy by division. One bacterium becomes two. Then two divide into four; the four divide into eight and so on. For certain strains of bacteria, the time for this division process is one minute.

a. If you put one of these bacterium in a botle at 11:00 p.m., the entire bottle will be full by midnight. When would the bottle be half full?

b. How do you know?

c. suppose you could be a bacterium in this bottle. At what time would you first realize that you were running out of space?

d. Suppose that at 11:58 some bacteria realize that they are running out of space in the bottle. So they launch a search for new bottles. They look far and wide, and finally, offshore in the Arctic Ocean, they find three new empty bottles. Great sighs of relief come from all the bacteria. This is three times the number of bootles they’ve known. Surely, they think, their space problems are over. Is that so?

Since their space resources have quadrupled, how long can their growth continue.