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The number at the top is how many half-lives have elapsed.Note the consequence of the law of large numbers: with more atoms, the overall decay is more regular and more predictable.In a medical context, the half-life may also describe the time that it takes for the concentration of a substance in blood plasma to reach one-half of its steady-state value (the "plasma half-life").The relationship between the biological and plasma half-lives of a substance can be complex, due to factors including accumulation in tissues, active metabolites, and receptor interactions.As an example, the radioactive decay of carbon-14 is exponential with a half-life of 5,730 years.A quantity of carbon-14 will decay to half of its original amount (on average) after 5,730 years, regardless of how big or small the original quantity was.Note that after one half-life there are not exactly one-half of the atoms remaining, only approximately, because of the random variation in the process.Nevertheless, when there are many identical atoms decaying (right boxes), the law of large numbers suggests that it is a very good approximation to say that half of the atoms remain after one half-life.
The term is commonly used in nuclear physics to describe how quickly unstable atoms undergo, or how long stable atoms survive, radioactive decay.
After another 5,730 years, one-quarter of the original will remain.
On the other hand, the time it will take a puddle to half-evaporate depends on how deep the puddle is.
Mathematically, the sum of two exponential functions is not a single exponential function.
A common example of such a situation is the waste of nuclear power stations, which is a mix of substances with vastly different half-lives.