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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 ...
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.
Doubling time. The doubling time is the time it takes for a population to double in size/value. It is applied to population growth, inflation, resource extraction, consumption of goods, compound interest, the volume of malignant tumours, and many other things that tend to grow over time. When the relative growth rate (not the absolute growth ...
The Euler–Lotka equation, derived and discussed below, is often attributed to either of its origins: Euler, who derived a special form in 1760, or Lotka, who derived a more general continuous version. The equation in discrete time is given by. where is the discrete growth rate, ℓ ( a) is the fraction of individuals surviving to age a and b ...
Compound annual growth rate ( CAGR) is a business, economics and investing term representing the mean annualized growth rate for compounding values over a given time period. [1] [2] CAGR smoothes the effect of volatility of periodic values that can render arithmetic means less meaningful. It is particularly useful to compare growth rates of ...
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The Monod equation is a mathematical model for the growth of microorganisms. It is named for Jacques Monod (1910–1976, a French biochemist, Nobel Prize in Physiology or Medicine in 1965), who proposed using an equation of this form to relate microbial growth rates in an aqueous environment to the concentration of a limiting nutrient. [1] [2 ...
The Harrod–Domar model makes the following a priori assumptions: 1: Output is a function of capital stock only (labor is irrelevant). 2: The marginal product of capital is constant; the production function exhibits constant returns to scale. This implies capital's marginal and average products are equal. 3: Capital is necessary for output.