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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.
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 ...
Weissberger's model. Weissberger’s modified exponential decay model, or simply, Weissberger’s model, is a radio wave propagation model that estimates the path loss due to the presence of one or more trees in a point-to-point telecommunication link. This model belongs to the category Foliage or Vegetation models.
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 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 ...
Lotka–Volterra equations. The Lotka–Volterra equations, also known as the Lotka–Volterra predator–prey model, are a pair of first-order nonlinear [disambiguation needed] differential equations, frequently used to describe the dynamics of biological systems in which two species interact, one as a predator and the other as prey.
In physics and engineering, the time constant, usually denoted by the Greek letter τ (tau), is the parameter characterizing the response to a step input of a first-order, linear time-invariant (LTI) system. [1] [note 1] The time constant is the main characteristic unit of a first-order LTI system. In the time domain, the usual choice to ...
The plateau principle is a mathematical model or scientific law originally developed to explain the time course of drug action ( pharmacokinetics ). [1] The principle has wide applicability in pharmacology, physiology, nutrition, biochemistry, and system dynamics. It applies whenever a drug or nutrient is infused or ingested at a relatively ...