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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.In nuclear physics, the Bateman equation is a mathematical model describing abundances and activities in a

**decay**chain as a function of time, based on the**decay**rates and initial abundances. The model was formulated by Ernest Rutherford in 1905 [1] and the analytical solution was provided by Harry Bateman in 1910. [2]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 ...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 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.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 ...Monod equation. 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 ...Exponential

**decay**. A quantity undergoing exponential**decay**. Larger**decay**constants make the quantity vanish much more rapidly. This plot shows**decay**for**decay**constant ( λ) of 25, 5, 1, 1/5, and 1/25 for x from 0 to 5. A quantity is subject to exponential**decay**if it decreases at a rate proportional to its current value.