Algebra II Decay Problems
1. A certain radioactive substance decays from 66,560 grams to 6.5 grams in 16 days. What is the half-life?2. Carbon-14 has a half-life of 5730 years. Organic objects contain carbon-14, as well as non-radioactive carbon, in known proportions. When an organism dies, it takes in no more carbon. The caron-14 decays, changing the proportions of the kinds of carbon in the organism. By determining the amount of carbon-14, it is possible to determine how long the organism has been dead, hence how old it is.
2a. How old is an animal bone that has lost 30% of its carbon-14?
2b. A mummy discovered in the pyramid Khufu in Egypt had lost 46% of its carbon-14. Determine its age.
3. The Statue of Zeus at Olympia, in Greece, is one of the seven wonders of the world. It is made of gold and ivory. The ivory was found to have lost 35% of its carbon-14. Determine the age of the statue (See Problem 2).
4. The half-life of Radon-222 is 3.8 days. How much of a supply of 1000 grams will remain after 30.4 days?
5. The half-life of Radium-226 is 1620 years. Of a sample of 351 grams, how much remains at the end of 4860 years?
6. Eighty-eight grams of the synthetic element Berkelium is found to decay radioactively to 56 g in 3h. If this decay is exponential, what is the half-life of Berkelium?
7. Find k for a radioactive element for which half of a 20 milligram sample remains after 9 years.
8. Radium-226 decomposes radioactively. Its half-life (the time half the sample takes to decompose) is 1800 years. Find the constant k for the decay formula. Use 100 grams as the original amount.