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Re: [Phys-l] Bacteria problem



On Jan 4, 2008, at 11:55 AM, Savinainen Antti wrote:

Hi again!

I seem to be asking a lot of question these days...this one is not physics but it may be of interest to some of you. I'm not asking for a full solution; a scenario of a possible solution would be nice.

I'll give you a bit backgound info on the problem. It was stated by a 13 year old student. He has been receiving informal teaching on high school mathematics and beyond given by our proficient IB students, one hour per week, since he was 8 years old. The student took his first university course on mathematics (calculus) last year. His problem goes like this:

"When modelling bacterial growth, it is often assumed that the bacteria have a certain "division time" (the time in which a single bacterial cell divides into two) that is constant, let's say 20 minutes. As it can be easily shown,this leads to an exponential increase in the number of bacteria. However, the "division time"
is definitely not constant in real life. What happens if
we assume that the "division time" is normally distributed with
a given mean and standard deviation, let's say with a mean of
20 minutes and a standard deviation of 5 minutes?
What kind of model would describe this situation, if
we also assume that the initial amount of bacterial cells is
quite small, let's say 2?"

I would expect the result to be exponential as well. It can be visualized as the sum of many exponential lines. Note that e^A +e^B+e^C = e^(A+B+C).
_______________________________________________________
Ludwik Kowalski, a retired physicist
5 Horizon Road, apt. 2702, Fort Lee, NJ, 07024, USA
Also an amateur journalist at http://csam.montclair.edu/~kowalski/cf/