Question 959158: Once upon a time, at precisely 11:00 pm, a single bacterium
was placed into a nutrient-filled bottle in a laboratory. The bacterium immediately began gobbling up
nutrients, and after just one minute-making the time 11:01- it had grown so much that it divided into
two bacteria. These two ate until, one minute later, they each divided into two bacteria, so that there
were a total of four bacteria in the bottle at 11:02. The four bacteria grew and divided into a total of
eight bacteria at 11:03, sixteen bacteria at 11:04, and so on. All seemed fine, and the bacteria kept on
eating happily and doubling their number every minute, until the “midnight catastrophe.” The
catastrophe was this: At the stroke of 12:00 midnight, the bottle became completely full of bacteria,
with no nutrients remaining- which meant that every single one of the bacteria was suddenly doomed to
death.
We now turn to our questions, as we seek to draw lessons from the tragic demise of the bacterial
colony.
Question 1: The catastrophe occurred because the bottle became completely full at 12:00 midnight.
When was the bottle half-full?
Question 2: You are a mathematically sophisticated bacterium, and at 11:56 you recognize the impending disaster. You immediately jump on your soapbox and warn that unless your fellow bacteria
slow their growth dramatically, the end is just 4 minutes away. Will anyone believe you?
Question 3: It’s 11:59 and your fellow bacteria are finally taking your warnings seriously. Hoping to
avert their impending doom, they quickly start a space program, sending little bacterial spaceships out
into the lab in search of new bottles. To their relief, they discover that the lab has three more bottles
that are filled with nutrients but have no one living in them. They immediately commence a mass
migration through with they successfully redistribute the population evenly among the four bottles (the
three new ones plus the one already occupied), just in time to prevent the midnight catastrophe. How
much more time do the additional bottles buy for their civilization?
Question 4: Because the three extra bottles bought so little time, the bacteria keep searching out more
and more bottles. Is there any hope that additional discoveries will allow the colony to continue its
rapid growth? Assume each bacterium occupies a volume of 10 with an exponent of -21;
cubic meters and the surface area of
the Earth is 510 million square km. At 1:00 a.m. how deep are the bacteria if they evenly spread over the surface of the earth?
Answer by mattsmom(1)   (Show Source):
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