Chapter 1.1, Problem 8E

In Exercises 6—10, we consider the phenomenon of radioactive decay which, from experimentation, we know behaves according to the law:
The rate at which a quantity of a radioactive isotope decays is proportional to the amount of the isotope present. The proportionality constant depends only on which radioactive isotope is used.

8. Carbon dating is a method of determining the time elapsed since the death of organicmaterial. The assumptions implicit in carbon dating are that
• Carbon 14 (C-14) makes up a constant proportion of the carbon that living matter ingests on a regular basis, and
• once the matter dies, the C-14 present decays, but no new carbon is added tothe matter.

Hence, by measuring the amount of C-14 still in the organic matter and comparing it to the amount of C-14 typically found in living matter, a "time since death" can be approximated. Using the decay-rate parameter you computed in Exercise 7, determine the time since death if

(a) 88% of the original C-14 is still in the material.
(b) 12% of the original C-14 is still in the material.
(c) 2% of the original C-14 is still in the material.
(d) 98% of the original C-14 is still in the material.

Remark: There has been speculation that the amount of C-14 available to living creatures has not been exactly constant over long periods (thousands of years). This makes accurate dates much trickier to determine.