The age of any remains from a once-living organism can be determined by radiocarbon dating, a procedure that works by determining the concentration of radioactive ¹⁴C in the remains. All living organisms contain an equilibrium concentration of radioactive ¹⁴C that gives rise to an average of 15.3 nuclear decay events per minute per gram of carbon. At death, however, no additional ¹⁴C is taken in, so the concentration slowly drops as radioactive decay occurs. What is the age of a bone fragment from an archaeological dig if the bone shows an average of 2.3 radioactive events per minute per gram of carbon? Radioactive decay is kinetically a first-order process, and t_1/2 for ¹⁴C is 5730 years.