Do you beleive this?

Question

Bacteria grow very quickly.
They reproduce about every 20 minutes.

It has been estimated that if unlimited space and food were avaliable for a single bacterium, after 2 days of reproduction there would be a mass about 4000 times that of the Earth.

yeah right!! anyone with me?

Answer 1

Maybe under ideal conditions but nothing is ever ideal.

Answer 2

There would also have to be unlimited space and food for each of the new bacteria. But that's not possible, because the bacteria would bump into each other, which means that there is no space or food on the side where there is another bacteria. So in fact, practically all the new bacteria die without fissioning.

It is true that many types of bacteria reproduce (fission) about every 20 minutes, if there is food and space. If all the bacteria lived, then after 2 days they would have fissioned 144 times.
2^144 = 2.23x10^43
If each bacteria has a mass of 10^-12 grams, then 2.23x10^43 bacteria has a mass of 2.23x10^31 grams, or about 4000 times Earth mass.

Answer 3

That's simple mathematics. If something reproduces once every twenty minutes, then (in a bacterium's case at least) it's making a copy of itself every twenty minutes. That's not where the high numbers come from. The copies are making copies of themselves. It's termed exponential growth. Under, as was previously stated, "ideal" circumstances, it seems possible. Three times an hour times twenty-four hours times two days is 144. So, that's 144 doublings, or two to the 144th. Try multiplying two times itself 144 times and you get the picture really quick. I personally don't know how much most bacteria weigh apiece, but I took an e. coli example from the internet and came up with this stuff. After two days of uninhibited reproduction on the order of one divide per bacterium (copies and original) per 20 minutes, a colony (of e. coli at least) would have a mass of 148.2 x 10^24 kilograms. The mass of the earth is 5.9742 × 10^24 kilograms. So, yes, your teacher was right, at least by my calculations.

Rather, let me say that it's extremely close and about another hour would finish the job for being 4000 times the mass of the earth.

Answer 4

I believe it. It is math though, not biology. Of course for bacteria to grow to 4,000 times the mass of Earth there would have to be more than that in available food, plenty of water, ways to get rid of waste products and so on.

No, what this really is, is a demonstration of the power of a geometric progression. Each bacterium splits into two every 20 minutes, and there are 144 20 minute periods in 2 days, so there are 144 generations of bacteria splitting. That means after 20 minutes there are 2, after 40 minutes there are 4, after an hour there are 8, and so on, doubling the number every 20 minutes. After 2 days, which is 144 times 20 minutes, you have a number so big that I can't write it without scientific notation. It is a little more than 2 followed by 43 zeroes. Try it yourself on a calculator. Do 2 times 2, then times 2 again and keep doing "times 2" until you have done it 144 times. After 20 "times 2"s, you have 1,048,576. By they time you get to 35 "times 2"s, the number no longer fits on the calculator. If you have a scientific calculator, it will switch to scientific notation. After 144 "times 2"s, you have a number so large that, if it represented a number of bacteria, would be 4,000 times the mass of the Earth.

Answer 5

No, that's right. Assuming no barrier to reproduction, and a doubling every 20 minutes, it is easy enough to do the calculation.

Since they reproduce by dividing in two, if you start with one bacterium, twenty minutes later you will have 2, then 2x2 twenty minutes after that, then 2x2x2 twenty minutes after that. After one hour you have 2x2x2 = 2^3 = 8 bacterial cells.

48 hours gives you 2^(3x48) = 2^144 = 2.23x10^43 bacterial cells. That is:

22,300,000,000,000,000,000,000,000,000,000,000,000,000,000 bacteria.

A rough estimate of the mass of a single bacterium is one picogram, which is 10^15kg (0.000000000000001kg). So, multiply the mass by the number of cells and you get a mass of bacteria of 2.23x10^28kg.

Earth has a mass of about 6x10^24kg. Divide one by the other and you'll find that your mass of cells is about 4000 times greater than the mass of Earth.

However, in reality the bacterial colony would soon exhaust its suply of nutrients and stop dividing.

(Edited to point out that for some reason it's cut short my string of zeros in the number of bacterial cells. There should be 41 of them.)

Answer 6

Probably this is not the worst scenario. Can you imagine rabbits...I mean lots of rabbits, billions of rabbits reproducing themselves exponentually. This is just scaring.
BTW, one of the apocaliptic scenarios in future technology developments is an unlimited replication of nanorobots (with the size comparable to bacterium) with much worse consequences.
Hopefully this world remains in a kind of equilibrium so far.