Natural Logs ```Name: Dave E. Status: student Age: N/A Location: N/A Country: N/A Date: N/A ``` Question: Where is the value e, the base of the natural logarithms, found in nature? Replies: The number 'e' appears in many applications and circumstances in nature. It is so ubiquitous that listing all these in not practical. For some examples do an internet search on: "number e". I prefer the search engine www.google.com but you can use any one. As a generality ANY PROCESS in which the rate of change of a variable Y(x), delta Y(x)/delta x, is proportional to the value of Y(x) results in Y(x) being an exponential function of (x). That is: Y(x) = A*e^(k*x) where 'A' and 'k' can be either positive or negative depending upon the process. Some specific examples are the compounding of interest, and radioactive decay. Vince Calder The number 'e' occurs in many places in nature. Any process, of which there are many, where the rate of change is proportional to the amount of whatever is changing in the process will involve e^(some power or function. The rate of many chemical reactions is an example, as is the decay of radioactive nucleii. The temperature dependence of the vapor pressure of liquids is obeys an exponential law [Clausius Clapyeron equation]. The absorption of many substances by the body often obeys this dependence. The list is long. Vince Calder Click here to return to the Mathematics Archives

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