Carbon Dating Presumes That,as Long as a Plant or Animal $A = A _ { 0 } e ^ { - 0.0001213 t }$

Multiple Choice

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