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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.
Malthusian growth model A Malthusian growth model, sometimes called a simple exponential growth model, is essentially exponential growth based on the idea of the function being proportional to the speed to which the function grows. The model is named after Thomas Robert Malthus, who wrote An Essay on the Principle of Population (1798), one of the earliest and most influential books on ...
The exercise of working through this problem may be used to explain and demonstrate exponents and the quick growth of exponential and geometric sequences. It can also be used to illustrate sigma notation.
Relative growth rate (RGR) is growth rate relative to size - that is, a rate of growth per unit time, as a proportion of its size at that moment in time. It is also called the exponential growth rate, or the continuous growth rate.
e. -folding. In science, e-folding is the time interval in which an exponentially growing quantity increases by a factor of e; [1] it is the base- e analog of doubling time. This term is often used in many areas of science, such as in atmospheric chemistry, medicine and theoretical physics, especially when cosmic inflation is investigated.
The law of exponential growth can be written in different but mathematically equivalent forms, by using a different base, for which the number e is a common and convenient choice: Here, denotes the initial value of the quantity x, k is the growth constant, and is the time it takes the quantity to grow by a factor of e.
Classical nucleation theory (CNT) is the most common theoretical model used to quantitatively study the kinetics of nucleation. [1][2][3][4] Nucleation is the first step in the spontaneous formation of a new thermodynamic phase or a new structure, starting from a state of metastability. The kinetics of formation of the new phase is frequently ...
Logistic function. A logistic function or logistic curve is a common S-shaped curve (sigmoid curve) with the equation. where. is the carrying capacity, the supremum of the values of the function; is the logistic growth rate, the steepness of the curve; and. is the value of the function's midpoint.