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  2. Exponential decay - Wikipedia

    en.wikipedia.org/wiki/Exponential_decay

    Symbolically, this process can be expressed by the following differential equation, where N is the quantity and λ is a positive rate called the exponential decay constant, disintegration constant, [1] rate constant, [2] or transformation constant: [3]

  3. Rate equation - Wikipedia

    en.wikipedia.org/wiki/Rate_equation

    The tentative rate equation determined by the method of initial rates is therefore normally verified by comparing the concentrations measured over a longer time (several half-lives) with the integrated form of the rate equation; this assumes that the reaction goes to completion. For example, the integrated rate law for a first-order reaction is

  4. Time constant - Wikipedia

    en.wikipedia.org/wiki/Time_constant

    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.

  5. Radioactive decay - Wikipedia

    en.wikipedia.org/wiki/Radioactive_decay

    The decay rate, or activity, ... as the decay events follow one after another. The solution to this first-order differential equation is the function: () ...

  6. Biological half-life - Wikipedia

    en.wikipedia.org/wiki/Biological_half-life

    where k is the reaction rate constant. Such a decay rate arises from a first-order reaction where the rate of elimination is proportional to the amount of the substance: [39] =. The half-life for this process is [39] = ⁡.

  7. Plateau principle - Wikipedia

    en.wikipedia.org/wiki/Plateau_Principle

    Although these equations were derived to assist with predicting the time course of drug action, [1] the same equation can be used for any substance or quantity that is being produced at a measurable rate and degraded with first-order kinetics. Because the equation applies in many instances of mass balance, it has very broad applicability in ...

  8. Half-life - Wikipedia

    en.wikipedia.org/wiki/Half-life

    In this situation it is generally uncommon to talk about half-life in the first place, but sometimes people will describe the decay in terms of its "first half-life", "second half-life", etc., where the first half-life is defined as the time required for decay from the initial value to 50%, the second half-life is from 50% to 25%, and so on.

  9. Bateman equation - Wikipedia

    en.wikipedia.org/wiki/Bateman_equation

    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]