The longer a drug’s half-life is, the longer it takes for the body to eliminate a single dose. This is medically significant in many instances, because drugs can interact with one another, and because some can influence the success of a surgical operation. For example, the blood thinner warfarin is prescribed to people who are at risk of developing blood clots. A person who is preparing to undergo a surgical procedure must stop taking the drug several days in advance, to eliminate it from the body and reduce the risk of excessive bleeding during the operation.
The decay of a mixture of two or more materials which each decay exponentially, but with different half-lives, is not exponential. 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. Consider a mixture of a rapidly decaying element A, with a half-life of 1 second, and a slowly decaying element B, with a half-life of 1 year. In a couple of minutes, almost all atoms of element A will have decayed after repeated halving of the initial number of atoms, but very few of the atoms of element B will have done so as only a tiny fraction of its half-life has elapsed. Thus, the mixture taken as a whole will not decay by halves.