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  2. Exponential growth - Wikipedia

    en.wikipedia.org/wiki/Exponential_growth

    Often the independent variable is time. Described as a function, a quantity undergoing exponential growth is an exponential function of time, that is, the variable representing time is the exponent (in contrast to other types of growth, such as quadratic growth). Exponential growth is the inverse of logarithmic growth.

  3. Population dynamics - Wikipedia

    en.wikipedia.org/wiki/Population_dynamics

    This is the core assumption for geometric populations, because with it we are going to obtain a geometric sequence. Then we define the geometric rate of increase R = b t - d t to be the birth rate minus the death rate. The geometric rate of increase do not depend on time t, because both the birth rate minus the death rate do not, with our ...

  4. Geometric progression - Wikipedia

    en.wikipedia.org/wiki/Geometric_progression

    A geometric progression, also known as a geometric sequence, is a mathematical sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed number called the common ratio. For example, the sequence 2, 6, 18, 54, ... is a geometric progression with a common ratio of 3.

  5. Relationships among probability distributions - Wikipedia

    en.wikipedia.org/wiki/Relationships_among...

    The sum of n geometric random variables with probability of success p is a negative binomial random variable with parameters n and p. The sum of n exponential (β) random variables is a gamma (n, β) random variable. Since n is an integer, the gamma distribution is also a Erlang distribution.

  6. Exponential distribution - Wikipedia

    en.wikipedia.org/wiki/Exponential_distribution

    In probability theory and statistics, the exponential distribution or negative exponential distribution is the probability distribution of the distance between events in a Poisson point process, i.e., a process in which events occur continuously and independently at a constant average rate; the distance parameter could be any meaningful mono-dimensional measure of the process, such as time ...

  7. Power series - Wikipedia

    en.wikipedia.org/wiki/Power_series

    1.2 Geometric series, exponential function and sine. ... the power series of the sum or difference of the functions can be obtained by termwise addition and subtraction.

  8. Geometric distribution - Wikipedia

    en.wikipedia.org/wiki/Geometric_distribution

    The exponential distribution is the continuous analogue of the geometric distribution. Applying the floor function to the exponential distribution with parameter λ {\displaystyle \lambda } creates a geometric distribution with parameter p = 1 − e − λ {\displaystyle p=1-e^{-\lambda }} defined over N 0 {\displaystyle \mathbb {N} _{0}} .

  9. Exponential function - Wikipedia

    en.wikipedia.org/wiki/Exponential_function

    Exponential functions with bases 2 and 1/2. In mathematics, the exponential function is the unique real function which maps zero to one and has a derivative equal to its value. The exponential of a variable ⁠ ⁠ is denoted ⁠ ⁡ ⁠ or ⁠ ⁠, with the two notations used interchangeably.