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 30% as much ¹⁴C as a living organism, how old would you predict it to be? Round to the nearest year. A)28,040 years B)5715 years C)9926 years D)14,758 years E)100 years

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Quizplus · Accepted Answer

To find the age, solve the equation $0.3 = e^{-0.0001213t}$. Taking the natural logarithm of both sides gives $\ln(0.3) = -0.0001213t$. Solving for $t$ gives $t \approx 9926$ years.

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