How Many Generations Of Bacteria Would It Take To Surpass Mass Of Earth

[tmca185]

One cell of Vibrio natriegens has a dry mass of ca. 10-12g (ca 10 to the power of minus 12) and the total mass of Planet Earth is 5.9726 x 1024 kg, Assuming zero mortality calculate in how many bacteria generations this species would surpass the mass of Planet Earth

[jim360]

At each generation the total number/ mass of bacteria doubles. So all you need to do is multiply 10^(-12) by 2 until you reach 5.97*10^27 (accounting for the different units).

You can speed things up by noting that 2^10=1000-ish, so that every ten generations the mass grows by a thousand times.

[tandh]

what happens if the dettol factory explodes though?

[bhg481]

Since the growth is logarithmic this problem is solved most simply by using logs.

[beso]

Growth in this question is exponential but the answer is found using logs.

We need the log to base two of the number of bacteria to equal the Earth's mass (the product of the number of bacteria per kilogram and the mass of the Earth in kilograms).

There are 10^15 bacteria per kilogram.

The formula in Excel using round numbers.
=LOG(6*10^(15+24),2)

The answer is about 132.

[beso]

And since the question is "surpass" and 132 does not quite make it, we need 132 generations.

[beso]

133

[jim360]

Beso's answer gets the precise solution and you'll need to learn logarithms in the future and how they work for a whole host of problems. My approach has the advantage of avoiding much calculation beyond 13*10, so would also lead to the answer of 130-and-a-bit, and is also worth reading into.

https://en.wikipedia.org/wiki/Back-of-the-envelope_calculation

[mibn2cweus]

So about a day-and-a-half then?

[Togo]

Antibiotic resistance is a quickly growing, extremely dangerous problem. World health leaders have described antibiotic-resistant bacteria as "nightmare bacteria" that "pose a catastrophic threat" to people in every country in the world.

http://www.cdc.gov/features/AntibioticResistanceThreats/index.html
Were doomed I tell ye.

[Colmc54]

All I know is that bacteria will still be around long after we breed ourselves into extinction and all our haughty scientific and artistic achievements die with us. In that much they are vastly superior to us.

[Old_Geezer]

Simplicity is usually a less vulnerable form than sophisticated 'higher level' animal forms. Don't see it being much to do with achievements nor superiority.

[Colmc54]

You wouldn't Old Geezer for you to me always seem to be a wise and succinctly welcome voice in our discussions.
However it has to be said that the survivability of our species with all our advances in culture and science is more fragile than those of the unicellular bacteria who divide every fifteen minutes and treat our efforts in the form of antibiotics with the contempt they often deserve.

http://www.bbc.co.uk/news/health-34269315

[jim360]

I'd say we have at least a potential advantage over previous macroscopic species that we can be proactive when it comes to trying to adapt to changes, rather than just reactive -- at least to some extent. If, for example, a large object smashed into the Earth, we might have some hope of seeing it approaching, allowing us to stop it altogether or at least to mitigate the damage to the species (then again, we might still miss its approach, but at least there would be a chance). Or in the event of major climate changes caused by tectonic movements -- we could predict those, too, and attempt to respond accordingly. Finally, of course, given a long enough time we could leave the planet altogether. So humans have potential to be a long-lasting species.

Bacteria remain the champion, though.