bacteria problem
25 Aug 2006 01:30 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
mayoraaseiHave not done any maths since first year. My skills are severely rusted ==;;; Someone tell me whether there's a way in which the following are all satisfied?
1) If you wear earplugs for an hour, the bacteria in your ear increase 700 times.
2) The doubling time of Staphylococcus under optimal conditions is approximately 30 minutes. Doubling time of Streptococcus is approximately 25 minutes. These two bacteria predominate in the ear canal.
3) Assuming that without earplugs, in normal conditions, the amount of bacteria in your ear should remain constant, and that the bacteria are already in stationary phase (i.e. the growth rate is constant).
@_______@;;;;
Am making "preserved duck egg pork congee" =___=;;; What a mouthful in English. Am hungry~!
1) If you wear earplugs for an hour, the bacteria in your ear increase 700 times.
2) The doubling time of Staphylococcus under optimal conditions is approximately 30 minutes. Doubling time of Streptococcus is approximately 25 minutes. These two bacteria predominate in the ear canal.
3) Assuming that without earplugs, in normal conditions, the amount of bacteria in your ear should remain constant, and that the bacteria are already in stationary phase (i.e. the growth rate is constant).
@_______@;;;;
Am making "preserved duck egg pork congee" =___=;;; What a mouthful in English. Am hungry~!
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no subject
Date: 2006-08-25 10:35 am (UTC)no subject
Date: 2006-08-26 03:48 am (UTC)2) The doubling time of bacteria that lives in one's ears is approximately 20 minutes average, no matter what species.
In other words, after 60 minutes, even if the rate of increase is changed to maximum (i.e. instead of the constant amount/death=new produced, it is now "every bacteria that is newly produced lives"), there would only be 2^3 times more bacteria than the mixture of what you originally started off with, no matter the species.
...Which is why I don't think there can possibly be 700 times more bacteria in one's ears after 1 hour unless there's some mathematical loophole I've missed.
I'm not worried about it, it's just that I saw this claim on some "fun fact of the day" thing, and I was like, "but wait, there's only so fast that bacteria can multiply!"
no subject
Date: 2006-08-26 04:13 am (UTC)in that case if you want to see if it's possible to have 700 times more bacteria in an hour, go like this:
2^9=512
2^10=1024
700 is less than 2^10 and 700 is more than 2^9, so if there is some type of bacteria which doubles itself more than 9 times in one hour (what's 60/9? ..hmm.. 20/3 .. erm, .. eeerrrmm.. almost 7. yeah. that. my arithmetic sucks) then you can have 700 times more bacteria.
but it wouldn't be staa.. erm, or stree.. erm. yeah. and if your ear doesn't consist mainly of this "super fast doubling bacteria", then you'd need an even "faster to double" bacteria to increase the amount to 700 times by the next hour.
what's the fastest known rate that bacteria can multiply?
no subject
Date: 2006-08-26 04:25 am (UTC)Well apparently the fastest known rate is just under 10 minutes, but the important thing with that is that
1) if the enzyme copying DNA is driven so fast, it is more likely to make mistakes, and it is more likely that the bacteria produced will not live.
2) I'm not sure which bacteria it is though. Chances are they're not even found on the body.
=___=;;;;;;
It's probably "theoretically possible" with a whole bunch of assumptions that doesn't exist in real situations.
What's staa or stree? O__o;;;
no subject
Date: 2006-08-26 06:28 am (UTC)staa and stree are my way of quietly indicating that I have no idea how to spell staphylococcus and streptococcus without copying and pasting :D