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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 ...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 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 ...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.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 ...Half-life (symbol t½) is the time required for a quantity (of substance) to reduce to half of its initial value. The term is commonly used in nuclear physics to describe how quickly unstable atoms undergo radioactive

**decay**or how long stable atoms survive. The term is also used more generally to characterize any type of exponential (or, rarely ...The stretched exponential function. is obtained by inserting a fractional power law into the exponential function. In most applications, it is meaningful only for arguments t between 0 and +∞. With β = 1, the usual exponential function is recovered. With a stretching exponent β between 0 and 1, the graph of log f versus t is ...