Guide to Logarithms and "e" in Nature

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Logarithms, particularly natural logarithms (log base e), frequently appear in mathematical solutions and various natural phenomena. Euler's number (e) is significant in processes where the rate of change is proportional to the quantity itself, such as radioactive decay and population growth models. It also plays a crucial role in Newton's Law of Cooling and in the continuous compounding of interest. Additionally, e is involved in the attenuation of wave intensity across different mediums. Understanding these applications highlights the relevance of e in both mathematics and the natural world.
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I am currently learning about logarithms and I understand that Log base e (or Ln) comes up quite often in solutions of logarithms

However, I also heard that it is a number that comes up often in nature

Are there any good examples of "e" in nature?

Anton
 
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Euler's number will arise in any process in which the rate of change of a quantity is proportional to the quantity itself. Radioactive decay, Newton's Law of Cooling, Population Growth models and continuous compounding of interest are a few examples.
 
Attenuation of wave intensity (light, sound, quantum etc.) when it is absorbed is another important example.
 

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