Talk:Bacterial growth

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The graph is certainly incorrect if "B" is supposed to look like exponential growth. Michael Hardy 22:49, 22 May 2004 (UTC)

It says:

At exponential phase, bacteria are reproducing at their maximum rate; therefore, their number increases during this phase. It is a period of exponential growth.

This is contradictory! It cannot be growing at its maximum rate while it's growing exponentially. See exponential growth. While something is growing exponentially, its growth rate is always increasing; it's never at its maximum growth rate. I can't help suspecting this of being a case of thinking that "exponential growth" merely means extremely or surprisingly rapid growth. Besides, the description makes it sound like the growth rate is jointly proportional to the present size and the amount by which the size falls short of the carrying capacity. That would make it approximately exponential in its early phases, but nowhere near exponential when the growth rate is maximum. Michael Hardy 20:36, 15 Jul 2004 (UTC)

If the number of bacteria is increasing exponentially, and each bacterium is reproducing at maximum rate, then the rate of increase can be increasing exponentially, no problems at all. RobertStar20 22:38, 2 Nov 2004 (UTC)

If what was meant was the each bacterium separately is reproducing at maximum rate, then the article is very unclear. Moreover, if each bacterium separately is reproducing faster at time t than at any other time, then one would expect slow per capita growth a later times, and therefore the growth rate is not exponential. In exponential growth, the per capita growth rate remains constant. If that varies, then growth is not exponential. Michael Hardy 22:44, 2 Nov 2004 (UTC)

If all the individual bacterium are separately reproducing at maximum rate, then the whole colony is at its maximum rate at that point in time, i.e. it is incapable of reproducing any faster. However, I agree that the per capita growth rate at later times will be slower, so it is indeed not technically exponential. Looking at the exponential growth page, maybe the logistic function is what it really is... but isn't this a bit too mathematical perhaps? We need a word which means increasing at an increasing rate, but not necessarily exponentially. As for the graph being incorrect, it's a log y-axis, so an exponential curve will become straight... if only it were actually exponential :-). [Unrelated question: do your comments on this page automatically appear on my talk page or what?] RobertStar20 23:19, 2 Nov 2004 (UTC)

I'm not entirely happy with the way this now reads; I'd like to see something more explicit about the mathematical model before such a phrase as "exponential growth" is used in a way that makes it appear to be meant literally. But maybe no one who knows this material has worked on this article. Michael Hardy 21:07, 8 Nov 2004 (UTC)

Bacteria definetly grow exponentially. The example of growing bacteria are used constantly to introduce, reinforce and evaluate understanding in high school math courses of exponential functions. Each bacteria has a period during which it will divide. Obviously, conditions such as space, food supply, heat, light, etc... affect this rate, so we assume those factors are constant. Suppose a given strain of bacteria, let's call it B1, divides every 4 hours. Assuming we start with say, 10 bacteria, and the conditions don't change, then you will have table as follows:

 Time (h)    Bacteria Count"

 0           10

 4           20

 8           40

 12          80

 16          160

 20          320

 24          640

 .           .

 .           .

 .           .

 This growth is modelled by the equation B = 10 x (2 ^ h/4),
  where B is the number of bacteria
  and h is the number of hours
  (x means multiply, ^ means exponent, / means divide)

So, the discussion is hopefully resolved with the accepted mathematical notion: Bacteria divide at a constant rate, hence their population grows exponentially.

How could that resolve the issue when the article says they do NOT grow exponentially? Michael Hardy 00:12, 12 December 2005 (UTC)

what you added to the article was utter nonsense. The point at which growth is fastest, after which it slows down, cannot be a time when it is growing exponentially. Michael Hardy 00:18, 12 December 2005 (UTC)

Sorry you feel that way. Perhaps i didn't explain it clearly? Or maybe I don't understand the confusion. Maybe someone could help me format the table above...or could you at least explain what you mean by utter nonsense? Do you mean my assumption that bacteria division is constant?

I just tried to reread your page, and it referenced the exponential growth page, which says, "Examples of exponential growth Biology. Microorganisms in a culture dish will grow exponentially, at first, after the first microorganism appears (but then logistically until the available food is exhausted, when growth stops). "

If we assume the division of bacteria occurs at a constant rate (environment, other factors are constant) then the number of bacteria in any population will grow exponentially. It's the same for many types of populations, from rabbits to humans. If you assume that there is a constant steady growth rate, then the number in a population grows exponentially over time.

Or put another way, without external stressors, a population size will grow exponentially over time.

Have I missed something? This concept is as old as Malthus at least, who, I believe, pointed out that a population grows exponentially but resources tend to grow linearly and hence each population will tend to exhaust it's resources, inevitably.

I'd sure like to understand better if there is something I'm missing, or something I'm not explaining well. I thought the confusion was whether or not bacteria divide exponentially. They don't, or at least, as far as i understand, the rate of division is constant for given environmental factors. But because they divide, they double there number every time, which gives rise to an exponential function (base 2).

I appreciate you taking the time to respond to my comments. Please remember I am very new to Wikipedia, and if I break ediquette I don't mean to. Jess.

http://www.cellsalive.com/ecoli.htm "LOG PHASE: Once the metabolic machinery is running, they start multiplying exponentially, doubling in number every few minutes."

http://www.ugrad.math.ubc.ca/coursedoc/math100/notes/zoo/andromed.html

http://www.abc.net.au/science/experimentals/stories/s1168046.htm "Bacteria double in numbers about every 20 minutes - that's exponential growth!"

Yes, you have missed something. What you missed is what this present article says. Bacteria do grow exponentially under some circumstances, but this article is entirely explicit that those are not the circumstances considered here. Michael Hardy 00:33, 6 January 2006 (UTC)

I can't believe you're being so difficult. I just looked again: it says "exponential phase" is when they're growing fastest. Obviously a misnomer. They're growing approximately exponentially only when they're growing much more slowly. Why don't you read what this article actually says? Michael Hardy 00:35, 6 January 2006 (UTC)