Carbon Dating Presumes That, as Long as a Plant or Animal

Carbon dating presumes that, as long as a plant or animal is alive, the proportion of its carbon that is ¹⁴C is constant.The amount of ¹⁴C in an object made from harvested plants, like paper, will decline exponentially according to the equation $A = A _ { 0 } e ^ { - 0.0001213 t }$ , where A represents the amount of ¹⁴C in the object, A_o represents the amount of ¹⁴C in living organisms, and t is the time in years since the plant was harvested.If an archeological artifact has 35% as much ¹⁴C as a living organism, how old would you predict it to be? Round to the nearest year.

A) 5715 years
B) 29,310 years
C) 93 years
D) 8655 years
E) 15,427 years