You have to determine the age of an ancient fabric sample. You burn a small piece of fabric in excess O₂, and pass the produced CO₂ through slaked lime (Ca(OH)₂) to produce a precipitate of CaCO₃. The radioactivity of a 0.545 g sample of CaCO₃ is 2.15×10⁻⁴ Bq. Given that the radioactivity of the sample is due to ¹⁴C which has a half-life of 5715 years and the radioactivity of recent samples is 15.3 disintegrations/min per gram carbon, how old is the fabric sample?