Search results
Results from the WOW.Com Content Network
Exponential growth. Exponential growth is a process that increases quantity over time at an ever-increasing rate. It occurs when the instantaneous rate of change (that is, the derivative) of a quantity with respect to time is proportional to the quantity itself. Described as a function, a quantity undergoing exponential growth is an exponential ...
This is the form of the equation that is most commonly used to describe exponential decay. Any one of decay constant, mean lifetime, or half-life is sufficient to characterise the decay. The notation λ for the decay constant is a remnant of the usual notation for an eigenvalue .
Exponential functions with bases 2 and 1/2. The exponential function is a mathematical function denoted by () = or (where the argument x is written as an exponent).Unless otherwise specified, the term generally refers to the positive-valued function of a real variable, although it can be extended to the complex numbers or generalized to other mathematical objects like matrices or Lie algebras.
Euler's formula, the definitions of the trigonometric functions and the standard identities for exponentials are sufficient to easily derive most trigonometric identities. It provides a powerful connection between analysis and trigonometry, and provides an interpretation of the sine and cosine functions as weighted sums of the exponential function:
Half-life (symbol t½) is the time required for a quantity (of substance) to reduce to half of its initial value. The term is commonly used in nuclear physics to describe how quickly unstable atoms undergo radioactive decay or how long stable atoms survive. The term is also used more generally to characterize any type of exponential (or, rarely ...
greater than 1, there will be exponential growth towards positive or negative infinity (depending on the sign of the initial term). 1, the progression is a constant sequence. between −1 and 1 but not zero, there will be exponential decay towards zero (→ 0). −1, the absolute value of each term in the sequence is constant and terms ...
To the right is the long tail, and to the left are the few that dominate (also known as the 80–20 rule ). In statistics, a power law is a functional relationship between two quantities, where a relative change in one quantity results in a relative change in the other quantity proportional to a power of the change, independent of the initial ...
Double exponential function. A double exponential function is a constant raised to the power of an exponential function. The general formula is (where a >1 and b >1), which grows much more quickly than an exponential function. For example, if a = b = 10: f (x) = 10 10x. f (0) = 10.