Re: can a bacterium reproduce to the weight of the earth in 24hrs?

Hi Julie,

The problem with your calculation above is that the bacterium takes 20 minutes to divide (and therefore form 2 bacteria), and that in another 20 minutes both these bacteria divide, so the number (and mass) of bacteria doubles 72 times a day. This is a lot.

Expressed mathematically, the formula for the mass of the bacterial population after t hours, where the mass of a single bacterium is m is:

m*2^(t*3)

That is m multiplied by 2 to the power of the number of 20 minute periods. In 2 hours, therefore the bacteria would have divided 6 times, first to give 2 bacteria, then 4, then 8, then 16, then 32, then 64. In 24 hours, the humber of bacteria would have doubled 72 times. giving a mass 2^ 72 times greater than that of a single baterium. This mass is equal to:

m* 4.72237*10^21 grams

The total mass after 24 hrs is therefore: 4.72237*10^9g.

This value is approximately 10^18 (a million million million) times less than the 5.9763*10^24 k. = 5.9763*10^27 g that the earth weighs. The bacteria would therefore take longer than 24 hours to weight as much as the earth, but not very much longer....

Solving the equation (10^-12) * 2^3x = 5.9763 * 10^27 simplified to 2^3x = 5.9763 * 10^39 tells us that it will only take 44.045 hours, or 44 hours, 2 minutes and 42 seconds for the bacteria to weigh as much as the earth. After 2 days (48 hours) the bacteria will weigh m*2^(48*3) grams = 2.23*10^28 kg. - 3731.5 times as much as the earth, more than all the planets in the solar system added together!!

Admin note: It's important to realize that bacterial cultures do not grow indefinitely. Eventually the microbes run out of nutrients and cannot proliferate at the exponential rate described above. In microbiologist terms, the culture is said to enter stationary phase. The growth rate slows, and eventually reaches a steady-state where the number of microbes dividing replaces those that die. Eventually, more bacteria die, from the lack of nutrients or toxins building up in the media, than are replaced by new cells. For this reason, a culture of bacteria could never grow to consume the full mass of the earth.

-L. Bry, MadSci Admin