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