Suppose that an egyptian farmer claims to have discovered a linen burial cloth used during egypt's middle kingdom some 4000 years ago. careful analysis shows that the cloth contains 80% of the 14c that it is estimated to have originally contained. how old is the cloth?

1844 years

Explanation:

¹⁴C follows a first-order beta-decay according to the following equation.

¹⁴C ⇒ ¹⁴N + β⁻

We can calculate the concentration of ¹⁴C after some time using the following expression.

where,

[C]t is the concentration of ¹⁴C after some time

[C]₀ is the original concentration of ¹⁴C

k is the rate constant

t is the time elapsed

We can calculate the rate constant if we know the half-life (t1/2) using the following expression.

Half-life of ¹⁴C is 5730 years. Then,

The elapsed time when the concentration of ¹⁴C is 80% of original is: