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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 ...
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.
Exponential-fed-batch culture Under ideal condition, cells grow exponentially. If the feed rate of the growth-limiting substrate is increased in proportion to the exponential growth rate of the cells, it is possible to maintain the cells' specific growth rate for a long time while keeping the substrate concentration in the culture liquid at a ...
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.
Gompertz function. 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 ...
Fed-batch fermentation is a variation of batch fermentation where some of the ingredients are added during the fermentation. This allows greater control over the stages of the process. In particular, production of secondary metabolites can be increased by adding a limited quantity of nutrients during the non-exponential growth phase.
List of exponential topics. This is a list of exponential topics, by Wikipedia page. See also list of logarithm topics . Accelerating change. Approximating natural exponents (log base e) Artin–Hasse exponential. Bacterial growth. Baker–Campbell–Hausdorff formula. Cell growth.
A logistic function or logistic curve is a common S-shaped curve ( sigmoid curve) with the equation. where. , the value of the function's midpoint; , the supremum of the values of the function; , the logistic growth rate or steepness of the curve. [1] Standard logistic function where. For values of in the domain of real numbers from to , the S ...