Determine the decimal amount remaining: 4.116=0.25625\frac{4.1}{16}=0.25625164.1=0.25625.
Determine the number of half-lives: (0.5)n=0.25625(0.5)^n=0.25625(0.5)n=0.25625,
nln0.5=ln0.25625, n=ln0.25625ln0.5=1.964376n \ln 0.5=\ln 0.25625,\,\,n=\frac{\ln 0.25625}{\ln 0.5}=1.964376nln0.5=ln0.25625,n=ln0.5ln0.25625=1.964376.
Determine years elapsed: 5715⋅n=11226.45715 \cdot n=11226.45715⋅n=11226.4 years.
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