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Half-life A more intuitive characteristic of exponential decay for many people is the time required for the decaying quantity to fall to one half of its initial value. (If N (t) is discrete, then this is the median life-time rather than the mean life-time.) This time is called the half-life, and often denoted by the symbol t1/2.
Half-life is constant over the lifetime of an exponentially decaying quantity, and it is a characteristic unit for the exponential decay equation. The accompanying table shows the reduction of a quantity as a function of the number of half-lives elapsed.
Exponential decay In exponential decay, such as of a radioactive isotope, the time constant can be interpreted as the mean lifetime. The half-life THL or T1/2 is related to the exponential decay constant by The reciprocal of the time constant is called the decay constant, and is denoted .
Equations for the approach to steady state Derivation of equations that describe the time course of change for a system with zero- order input and first-order elimination are presented in the articles Exponential decay and Biological half-life, and in scientific literature. [1][7]
Biological half-life (elimination half-life, pharmacological half-life) is the time taken for concentration of a biological substance (such as a medication) to decrease from its maximum concentration (C max) to half of C max in the blood plasma. [1][2][3][4][5] It is denoted by the abbreviation . [2][4] This is used to measure the removal of ...
The decay of an initial population of identical atoms over time t follows a decaying exponential distribution e−λt, where λ is the decay constant. An important property of a radioactive material is its half-life, the time by which half of an initial number of identical parent radioisotopes can be expected statistically to have decayed to their daughters, which is inversely related to λ ...
With the decay constant it is possible to calculate the effective half-life using the formula: The biological decay constant is often approximated as it is more difficult to accurately determine than the physical decay constant.
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.