A 1000 G Sample of Wood from an Archaeological Site Produced

A 10.00 g sample of wood from an archaeological site produced 3,072 $\beta$ particles in a 10-hour measurement owing to the presence of carbon-14, while a 10.00 g sample of new wood produced 9,216 $\beta$ particles in the same period of time. The half-life of carbon-14 is 5,730 years. How old is the wood from the archaeological site?

A) 5,730 years
B) 2,865 years
C) 4,040 years
D) 9,080 years
E) The correct answer differs by more than 100 years from the values given in A-D.