User:Pashute/E (mathematical constant)
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The number e is an important mathematical constant approximately equal to 2.71828,[1]
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e is the base rate of continuous growth which is any growing process in which each newly produced growth, itself grows at the same rate as the original growing object. Compound interest and Cell tissue growth are examples of continuous growth, as are many processes occurring in nature, and studied in economics, statistics, physics, chemistry and biology.
ex is the resulting quantity from continuous growth within x periods of time, at a rate of 100% initial growth (meaning that it would double itself withing the period of time, without the additional growth of the produced growth itself), so e is the resulting quantity after a single period of time.
e can be calculated, and defined mathematically in many ways.
Its definition stemming from continuous growth is:
Important to calculus, e can also be defined as the base of the logarithmic function logex which has a derivative slope of 1/x. That logarithmic function, which has a derivative of 1/x, is defined as the natural logarithm, marked as ln(x), and is called so because of abundantly occuring continuous growth in nature.
e is also the base of the exponential function e^x with of a derivative slope which is defined by the exponential function itself:
The numerical value of e truncated to 50 decimal places is