Given
The half life is T=5715 years
The initial amount is N=50 g
To find
1) How much of it remains after 1600 years?
(2) How much of it remains after 16000 years?
Explanation
The amount of carbon remains after t yaers is
[tex]N^{\prime}=N(\frac{1}{2})^{\frac{t}{T}}[/tex]
1. Thus putting t=1600 years
[tex]\begin{gathered} N^{\prime}=50(\frac{1}{2})^{\frac{1600}{5715}} \\ \Rightarrow N^{\prime}=41.208\text{ g} \end{gathered}[/tex]
2.Putting t=16000
[tex]\begin{gathered} N^{\prime}=50(\frac{1}{2})^{\frac{16000}{5715}} \\ \Rightarrow N^{\prime}=7.184\text{ g} \end{gathered}[/tex]
Conclusion
1.Amount remains after 1600 year is 41.208 g
2.Amount remains after 16000 year is 7.184 g
