## Naming or Defining types of Growth.

Complex numbers, rational functions, logarithms, sequences and series, matrix operations, etc.
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### Naming or Defining types of Growth.

I was in a discussion with a friend. I understand that Geometric growth and Exponential growth often amount to the same thing as mentioned in Wikipedia under 'exponential growth'. However, I thought 'exponential growth' is sometimes also called 'logarithmic growth' and in Wikipedia under 'bacterial growth' there is an associated discussion of exponential growth during a 'log phase'. Can population growth sometimes be synonymously called: geometric growth, exponential growth, and logarithmic growth? I just registered on "Purple Math" and like math but have found advanced math difficult. Thanks.

stapel_eliz
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"Exponential" growth is usually meant to be increasingly increasing; that is, it gets bigger faster and faster. Also, exponential growth generally has a fixed minimum, a horizontal line that it is never below. You can see a sampling of typical graphs at the bottom of this page.

"Logarithmic" growth is usually meant to be decreasingly increasing; that is, it gets bigger, but slower and slower. Also, logarithmic growth generally has a restricted domain, a vertical line that it never crosses. You can see a sampling of typical graphs at the bottom of this page.

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### Re: Naming or Defining types of Growth.

Thank you for the help. The Wikipedia article for "Bacterial Growth" does have a discussion that parallels what you just showed as well as said. Even if a growth curve has a rapidly increasing population 'log phase', that does not mean the rapidly doubling population is increasingly increasing -- or does it? Must there be an inflection point somewhere in a bacterial growth curve where (1) there is a single bacterium; (2) there is a stage of exponential growth with much doublings of the population; (3) there then begins a stage of logarithmic growth with gradual slowing due to limitations of growth perhaps from food supply or space; (4) then there may be a steady phase; and, (5) maybe even a declining phase.

Perhaps the Wikipedia article on "Bacterial Growth" was confusing one part of a curve which consisted of both exponential growth and logarithmic growth and calling it by one name. If the rate of doublings of the population are growing shorter and shorter, then do we have exponential growth? And, if the rate of doublings of the population are growing longer and longer, then do we have logarithmic growth?

Do the so-called 'sigmoid growth curves' consist of an exponential phase and a logarithmic phase? I hope this is an okay question to ask about in the "pre-calculus area." Or, is there a better name than "sigmoid"? Thanks again.

stapel_eliz
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Are you perhaps looking at "logistic" growth?

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### Re: Naming or Defining types of Growth.

Growth curves are probably "logistic" but the growth part may be both exponential and logarithmic and the decline part could be exponential and logarithmic too. Maybe with a logistic curve there is no inflection point. ??? I guess there is need for me to take a trip to the library or check further on the internet. Thanks. It is much clearer.