C-14 has a half life of 5730 years, an artifact gives 4 counts per minute on a detector, living matter gives a count of 32. What is the estimated age of the artifact?

17188 years

Explanation:

Given that;

0.693/t1/2 = 2.303/t log (Ao/A)

Where;

t1/2 = half life of carbon -14

t = time taken

Ao = activity of a living sample

A activity of the artifact

0.693/5730 = 2.303/t log (32/4)

1.21 * 10^-4 = 2.303/t * 0.9031

1.21 * 10^-4 = 2.0798/t

t = 2.0798/1.21 * 10^-4

t = 17188 years

a). in this case, dh> 0 and sd> 0. if t becomes larger, the term "-tds" will become more negative. at some point, it is possible that -dts will be more negative than the dh is positive, and the reaction will become spontaneous. this is probably the correct answer, but you should look at all of the other possibilities and make sure of that.