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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 function of time ...
The exponential function extends to an entire function on the complex plane. Euler's formula relates its values at purely imaginary arguments to trigonometric functions. The exponential function also has analogues for which the argument is a matrix, or even an element of a Banach algebra or a Lie algebra .
The doubling time is a characteristic unit (a natural unit of scale) for the exponential growth equation, and its converse for exponential decay is the half-life. As an example, Canada's net population growth was 2.7 percent in the year 2022, dividing 72 by 2.7 gives an approximate doubling time of about 27 years.
In finance, the rule of 72, the rule of 70 [1] and the rule of 69.3 are methods for estimating an investment 's doubling time. The rule number (e.g., 72) is divided by the interest percentage per period (usually years) to obtain the approximate number of periods required for doubling. Although scientific calculators and spreadsheet programs ...
RGR is a concept relevant in cases where the increase in a state variable over time is proportional to the value of that state variable at the beginning of a time period. In terms of differential equations, if is the current size, and its growth rate, then relative growth rate is. If the RGR is constant, i.e., a solution to this equation is.
The first block is a unit block and the dashed line represents the infinite sum of the sequence, a number that it will forever approach but never touch: 2, 3/2, and 4/3 respectively. 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 Gompertz curve or Gompertz function is a type of mathematical model for a time series, named after Benjamin Gompertz (1779–1865). It is a sigmoid function which describes growth as being slowest at the start and end of a given time period. The right-side or future value asymptote of the function is approached much more gradually by the ...
The Weibull plot is a plot of the empirical cumulative distribution function of data on special axes in a type of Q–Q plot. The axes are versus . The reason for this change of variables is the cumulative distribution function can be linearized: which can be seen to be in the standard form of a straight line.
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