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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 ...
Exponential decay is a scalar multiple of the exponential distribution (i.e. the individual lifetime of each object is exponentially distributed), which has a well-known expected value. We can compute it here using integration by parts.
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.
Radioactive decay (also known as nuclear decay, radioactivity, radioactive disintegration, or nuclear disintegration) is the process by which an unstable atomic nucleus loses energy by radiation. A material containing unstable nuclei is considered radioactive. Three of the most common types of decay are alpha, beta, and gamma decay.
First order LTI systems are characterized by the differential equation + = where τ represents the exponential decay constant and V is a function of time t = (). The right-hand side is the forcing function f(t) describing an external driving function of time, which can be regarded as the system input, to which V(t) is the response, or system output.
Effective half-life. In pharmacokinetics, the effective half-life is the rate of accumulation or elimination of a biochemical or pharmacological substance in an organism; it is the analogue of biological half-life when the kinetics are governed by multiple independent mechanisms. This is seen when there are multiple mechanisms of elimination ...
The natural logarithm of e itself, ln e, is 1, because e1 = e, while the natural logarithm of 1 is 0, since e0 = 1. The natural logarithm can be defined for any positive real number a as the area under the curve y = 1/x from 1 to a[4] (with the area being negative when 0 < a < 1). The simplicity of this definition, which is matched in many ...
Plateau principle. 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 ...