Compared with the fibers of cotton plants growing today, what is the relative ratio radioactivity in the old material vs the relative amount radioactivity in the new material? The half-life of 14C is 5730 y. (A0 = original radioactivity and At = current radioactivity). For a quipu sample that is 4800 years old, we will calculate the ratio of 14C/12C in the sample.
At/A0 = ?

0.56

Explanation:

From the formula;

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

t1/2 = half life of the C-14 = 5730 y

t = time elapsed = 4800 y

At = Activity of C-14 at time t

Ao= Activity of a living C-14 sample

0.693/5730 = 2.303/4800 log (Ao/At)

1.2 * 10^-4 = 4.8 * 10^-4 log (Ao/At)

log (Ao/At) = 1.2 * 10^-4/4.8 * 10^-4

log (Ao/At) = 0.25

Ao/At = Antilog (0.25)

Ao/At = 1.778

Hence;

At/Ao = (1.778)^-1

At/Ao = 0.56

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