The burial cloth of an Egyptian is estimated to contain S9 o

The burial cloth of an Egyptian is estimated to contain S9% of the carbon. 14 it contained originally. How long ago was the mummy buried? (The half-lre of carbon-14 is 5730 years) Growth constant kw ,L How long ago was it buried? years Calculate the answer to the nearest interger

Solution

The fraction of C-14 remaining at time t years is given by A(t) = (1/2)^(t/5730).

A(t) = (1/2)^(t/5730) = 0.59.

Taking logs of both sides:
log(0.59) = log((1/2)^(t/5730)) = (t/5730) log(1/2).
t = 5730 log(0.59) / log(1/2) = 4360 years, to the nearest ten years.