bacteria problem

[mayoraasei]

Have 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~!

Comments

[jezjezjezza.livejournal.com]

I don't think you can satisfy both 1 and 3 because you can't wear earplugs and not wear earplugs at the same time. do you mean "plug one ear and let the other one be unpluggled"?

oh fenglet, your cooking skills induce jealousy *pout* :)

[luna-rainbow.livejournal.com]

Hmm? So number 1 and 2 can be satisfied? O__o;

3 is just there as an assumption saying that bacteria amount is constant instead of decreasing, so that even a sharp increase when wearing earplugs would only be compared to the constant amount rather than a decreasing amount? @___@ Is confused.

[jezjezjezza.livejournal.com]

oh ok.. *pause* *faints* I'm confused too XD

(if we call the amount of bacteria we have initally X)

1 says that wearing earplugs (for an hour) makes us end up with 700X bacteria

2 says that Staphylococcus will double in 30 minutes if we have optimal conditions, and that Streptococcus will double in 25 minutes under optimal conditions..

erm, ok.. uum, suppose we initially have A amounts of staphylococcus, and B amounts of streptococcus, and C amounts of whatever isn't either of those..

then A+B+C = X, so if we have condition (1), we know that we will end up with 700X = aA +bB +cC, whatever a, b and c are (not necessarily 700 since the different bacteria would grow at different rates)..

*faints* erm.. since we don't know whether wearing earplugs provides optimal conditions, condition (2) doesn't give us enough info.

if we assume wearing earplugs provides optimal conditions, then the staphylococcus will have doubled once in the first half hour (A--> 2A) and then again in the next (2A-->4A) so 700X = 4A + bB +cC..

and the streptococcus.. oh crap, I forgot about all those growth model thingos.. I haven't done much applied maths..

^__^ sorry fenglet, I can't help any more than that +_+

[siu.livejournal.com]

Woah, what a start... Don't think I can add much to it.. but growth models.. Hmm... >__>;; Exponentially or linearly... >_>;;; Let's see... Very much like jaz's, plus.. i lack sleeep. Hmm...

1) If you wear earplugs for an hour, the bacteria (X) in your ear increase 700 times.

Basic: 1 hr = 60 mins = X * 700 bacteria

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.

Assuming that wearing earplugs is optimal conditions because its nice and warm...

Let Stap = A
and Stre = B
and others = C

Soo.... In 0.5 hrs = 30 minutes = A -> 2A
In errr... 25/60 hrs or 25 mins = B -> 2B
C, if there is one = C -> ?C (say cC)

So, in one hour (i.e. 60 minutes)... 700X = (60/30)*2A + (60/25)*2B + (60/?) * cC = 4A + 4.8B + cC
Or... X = (4A + 4.8B + cC)/700

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).

Err... so... if its normal condition... then regardless of time, A -> A and B -> B, etc, because I am assuming that where there is growth, there will be decay as well, otherwise, you might be getting accumulation... >__>;;;

I don't know what exactly you want to satisfy though... >__>;;; *lost*

[jezjezjezza.livejournal.com]

btw fenglet, what's this for? are you worried about earplugs?

[luna-rainbow.livejournal.com]

Okay, the way I looked at this problem was:

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!"

[jezjezjezza.livejournal.com]

oh I see!

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?

[luna-rainbow.livejournal.com]

Ah I see I see!!!

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;;;

[jezjezjezza.livejournal.com]

hehehe, yeah a lot of things are possible in theory :D hehehehe..

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