1. Applications

2. The half-life of a radioactive substance is the time it takes for half of the atoms of the substance to become disintegrated. All life on Earth contains the radioactive element Carbon-14, which decay continuously at a fixed rate. The half-life of Carbon-14 is 5760 years. That is, every 5760 years half of a mass of Carbon-14 decays away. Suppose that bones of a woolly mammoth are estimated to contain only 3% as much Carbon-14 as they would have contained when the animal was alive. How long ago did the mammoth die?

3. Carbon-14 solution As with previous modeling, a table of values will help us develop a model. Time (t) Amount of C-14 remaining (y)

4. Carbon-14 solution As with previous modeling, a table of values will help us develop a model. Time (t) Amount of C-14 remaining (y)

5. Carbon-14 solution As with previous modeling, a table of values will help us develop a model. Time (t) Amount of C-14 remaining (y) 5760

6. Carbon-14 solution As with previous modeling, a table of values will help us develop a model. Time (t) Amount of C-14 remaining (y) 5760

7. Carbon-14 solution As with previous modeling, a table of values will help us develop a model. Time (t) Amount of C-14 remaining (y) 5760 ???

8. Carbon-14 solution As with previous modeling, a table of values will help us develop a model. Time (t) Amount of C-14 remaining (y) 5760 ???

9. Carbon-14 solution As with previous modeling, a table of values will help us develop a model. Time (t) Amount of C-14 remaining (y) 5760 ???

10. Carbon-14 solution As with previous modeling, a table of values will help us develop a model. Time (t) Amount of C-14 remaining (y) 5760 ???

11. Carbon-14 solution As with previous modeling, a table of values will help us develop a model. Time (t) Amount of C-14 remaining (y) 5760 ???

12. Carbon-14 solution As with previous modeling, a table of values will help us develop a model. Time (t) Amount of C-14 remaining (y) 5760 ???

13. Carbon-14 solution As with previous modeling, a table of values will help us develop a model. Time (t) Amount of C-14 remaining (y) 5760 ???

14. Carbon-14 solution As with previous modeling, a table of values will help us develop a model. Time (t) Amount of C-14 remaining (y) 5760 ???

15. Carbon-14 solution As with previous modeling, a table of values will help us develop a model. Time (t) Amount of C-14 remaining (y) 5760 ???

16. Carbon-14 solution As with previous modeling, a table of values will help us develop a model. Time (t) Amount of C-14 remaining (y) 5760 ???

17. Carbon-14 solution As with previous modeling, a table of values will help us develop a model. Time (t) Amount of C-14 remaining (y) 5760 ???

18. Carbon-14 solution As with previous modeling, a table of values will help us develop a model. Time (t) Amount of C-14 remaining (y) 5760 ???

19. Carbon-14 solution As with previous modeling, a table of values will help us develop a model. Time (t) Amount of C-14 remaining (y) 5760 ???

20. Carbon-14 solution As with previous modeling, a table of values will help us develop a model. Time (t) Amount of C-14 remaining (y) 5760 ???

21. Carbon-14 solution As with previous modeling, a table of values will help us develop a model. Time (t) Amount of C-14 remaining (y) 5760 ???

22. Carbon-14 solution As with previous modeling, a table of values will help us develop a model. Time (t) Amount of C-14 remaining (y) 5760 ???

23. Carbon-14 solution As with previous modeling, a table of values will help us develop a model. Time (t) Amount of C-14 remaining (y) 5760 ???

24. Carbon-14 solution As with previous modeling, a table of values will help us develop a model. Time (t) Amount of C-14 remaining (y) 5760 ???

25. Carbon-14 solution As with previous modeling, a table of values will help us develop a model. Time (t) Amount of C-14 remaining (y) 5760 ???

26. Carbon-14 solution As with previous modeling, a table of values will help us develop a model. Time (t) Amount of C-14 remaining (y) 5760 ???

27. Carbon-14 solution As with previous modeling, a table of values will help us develop a model. Time (t) Amount of C-14 remaining (y) 5760 ???

28. Carbon-14 solution As with previous modeling, a table of values will help us develop a model. Time (t) Amount of C-14 remaining (y) 5760 ???

29. Carbon-14 solution As with previous modeling, a table of values will help us develop a model. Time (t) Amount of C-14 remaining (y) 5760 ??? The mammoth died approximately 29,000 years ago.

30. Sodium-22 Example The half-life of Sodium-22 is 2.6 years. A geologist examining a meteorite estimates that it contains only about 10% as much Sodium-22 as it would have contained when it reached Earth’s surface. How long ago did the meteorite reach the surface of Earth?

31. Sodium-22 Example The half-life of Sodium-22 is 2.6 years. A geologist examining a meteorite estimates that it contains only about 10% as much Sodium-22 as it would have contained when it reached Earth’s surface. How long ago did the meteorite reach the surface of Earth? Time (t) Amount of Na-22 remaining (y) 2.6 ???

32. Sodium-22 Example The half-life of Sodium-22 is 2.6 years. A geologist examining a meteorite estimates that it contains only about 10% as much Sodium-22 as it would have contained when it reached Earth’s surface. How long ago did the meteorite reach the surface of Earth? Time (t) Amount of Na-22 remaining (y) 2.6 ???

33. Sodium-22 Example The half-life of Sodium-22 is 2.6 years. A geologist examining a meteorite estimates that it contains only about 10% as much Sodium-22 as it would have contained when it reached Earth’s surface. How long ago did the meteorite reach the surface of Earth? Time (t) Amount of Na-22 remaining (y) 2.6 ???

34. Sodium-22 Example The half-life of Sodium-22 is 2.6 years. A geologist examining a meteorite estimates that it contains only about 10% as much Sodium-22 as it would have contained when it reached Earth’s surface. How long ago did the meteorite reach the surface of Earth? Time (t) Amount of Na-22 remaining (y) 2.6 ???

35. Sodium-22 Example The half-life of Sodium-22 is 2.6 years. A geologist examining a meteorite estimates that it contains only about 10% as much Sodium-22 as it would have contained when it reached Earth’s surface. How long ago did the meteorite reach the surface of Earth? Time (t) Amount of Na-22 remaining (y) 2.6 ???

36. Assignment Radioactive Dating – Uranium-235 is one of the radioactive elements used in estimating the age of rocks. The half life of U-235 is 703.8 million years. A rock found in the Australian Outback is estimated to have 20% of the U-235 it had when it was formed. What is the age of the rock?