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.

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The given equation can be rewritten as: A = A₀ (0.7)^(t/5730) where A₀ is the initial amount of ¹⁴C in the living organism (100%), and 5730 is the half-life of ¹⁴C. We are told that the artifact has 30% as much ¹⁴C as a living organism, which means: 0.3A₀ = A₀ (0.7)^(t/5730) Simplifying, we get: 0.7^(t/5730) = 0.3 Taking the natural logarithm of both sides, we get: (t/5730) ln(0.7) = ln(0.3) Solving for t, we get: t ≈ 9926 years Rounding to the nearest year, we get: Answer: C (9926 years)

Carbon Dating Presumes That,as Long as a Plant or Animal A=A0e−0.0001213tA = A _ { 0 } e ^ { - 0.0001213 t }A=A0​e−0.0001213t

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