Answer:
The age of the sample is 4224 years.
Explanation:
Let the age of the sample be t years old.
Initial mass percentage of carbon-14 in an artifact = 100%
Initial mass of carbon-14 in an artifact = [tex][A_o][/tex]
Final mass percentage of carbon-14 in an artifact t years = 60%
Final mass of carbon-14 in an artifact = [tex][A]=0.06[A_o][/tex]
Half life of the carbon-14 = [tex]t_{1/2}=5730 years[/tex]
[tex]k=\frac{0.693}{t_{1/2}}[/tex]
[tex][A]=[A_o]\times e^{-kt}[/tex]
[tex][A]=[A_o]\times e^{-\frac{0.693}{t_{1/2}}\times t}[/tex]
[tex]0.60[A_o]=[A_o]\times e^{-\frac{0.693}{5730 year}\times t}[/tex]
Solving for t:
t = 4223.71 years ≈ 4224 years
The age of the sample is 4224 years.
