A wooden spear shaft recovered from an archaeological site shows an activity of 3.5 disintegrations per second per gram due to the presence of radioactive 14C. Fresh living wood of the same mass exhibits an activity of 15.6 disintegrations per second per gram. The half-life of 14C is 5730years.
(i) Write the mathematical relation between activity and time for a radioactive nuclide that will allow the age of the sample to be determined.
(ii) Hence calculate the age of the spear shaft, giving your answer correct to the nearest decade.