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  2. Exponential growth - Wikipedia

    Exponential growth is a process that increases quantity over time. 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 function of time, that is, the variable ...

  3. Exponential decay - Wikipedia

    Exponential decay. A quantity undergoing exponential decay. Larger decay constants make the quantity vanish much more rapidly. This plot shows decay for decay constant ( λ) of 25, 5, 1, 1/5, and 1/25 for x from 0 to 5. A quantity is subject to exponential decay if it decreases at a rate proportional to its current value.

  4. Half-life - Wikipedia

    The term is also used more generally to characterize any type of exponential (or, rarely, non-exponential) decay. For example, the medical sciences refer to the biological half-life of drugs and other chemicals in the human body. The converse of half-life (in exponential growth) is doubling time.

  5. Exponential function - Wikipedia

    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.

  6. Biological exponential growth - Wikipedia

    Biological exponential growth. Biological exponential growth is the unrestricted growth of a population of organisms, occurring when resources in its habitat are unlimited. Most commonly apparent in species that reproduce quickly and asexually, like bacteria, exponential growth is intuitive from the fact that each organism can divide and ...

  7. e (mathematical constant) - Wikipedia

    If f(t) is an exponential function, then the quantity = / ′ is a constant, sometimes called the time constant (it is the reciprocal of the exponential growth constant or decay constant). The time constant is the time it takes for the exponential function to increase by a factor of e : f ( t + τ ) = e f ( t ) {\displaystyle f(t+\tau )=ef(t)} .

  8. Natural logarithm - Wikipedia

    The natural logarithm of a number is its logarithm to the base of the mathematical constant e, which is an irrational and transcendental number approximately equal to 2.718 281 828 459. The natural logarithm of x is generally written as ln x, loge x, or sometimes, if the base e is implicit, simply log x. [1] [2] Parentheses are sometimes added ...

  9. Geometric progression - Wikipedia

    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 ...

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