Baffling bacteria math problem?

Question

The bacteria can reproduce every 20 minutes. At the end of 24 hours the bacteria would have a mass of 2 million pounds. Needless to say, this could not really happen. If the bacteria affected you at noon and it reproduced, every 20 minutes, at approximately what time would the bacteria outweigh you?

(I weight 120 puounds)

Answer 1

although at perfect conditions, some bacteria might be able to have a generation time of 20 minutes, that is not to say that they do actually reproduce every 20 minutes.  as they consume lots of resources, and become surrounded by other bacteria, are up "against a wall", or in their own waste, etc-then they stop reproducing.

but to do the fun part of your math problem, lets say that a bacteria weighs about 1/5,200,000,000,000 of a gram, which would be the weight per bacterium if 1 bacteria becomes 2 million pounds of bacteria at 24 hours by doubling every 20 minutes.  so 5 trillion bacteria would weigh one gram.  if you start with 1 bacteria, and assume a doubling time of 20 minutes, then there would be 5 trillion bacteria after 14 hours, weighing one gram.  then you would need 454 grams to weigh one pound, so you would need 454 x 5 trillion bacteria to weigh one pound, and this would happen at about 17 hours.  now you need to have 120 pounds, so you need 454 x 5 trillion x 120, or 270 quadrillion bacteria.  this occurs 19 hours and 20 minutes, so it takes about 19:20 to reach 120 pounds.

remember that i assumed a weight of one 5 trillionth of a gram, based on your 2 million pound estimate for 24 hours. it might be 5 quadrillionths of a gram, in which case you would need 1000 times as many bacteria, which would happen 3 hours and 20 minutes later, at 22:40 hours.  so you need to adjust for the actual weight of the bacteria that you are using, but there are about 1000 times as many every 3 hours and 20 minutes.

once again, they dont really double every 20  minutes, they only do under perfect conditions with unlimited resources.