For Exercises 29–36, refer to the following. The physical half-life of a radioactive substance is unaffected by the biochemistry inside the human body. However, such a substance may not remain in the body for good but instead be excreted at some rate, thereby reducing the radiation exposure. The rate of excretion can be expressed in the form of a biological half-life. Let the physical half-life be and the biological half-life be . Then a combined effective half-life can be calculated from

The two paths for eliminating the radioisotope act in parallel. In mathematical terms, is one-half the harmonic mean of the two half-lives (Chapter 19, Exercise 16). Sometimes physical decay is the dominant influence (Exercises 29–31) and sometimes biological clearing is (Exercise 32).