c
\(\frac{{^{14}{\text{C}}}}{{^{12}{\text{C}}}} = \frac{1}{{16}} = \frac{{\text{N}}}{{{{\text{N}}_0}}}\)

\(\because \frac{\mathrm{N}}{\mathrm{N}_{0}}=\left(\frac{1}{2}\right)^{\mathrm{n}}\)

\(\Rightarrow \quad \frac{1}{16}=\left(\frac{1}{2}\right)^{n} \Rightarrow\left(\frac{1}{2}\right)^{4}=\left(\frac{1}{2}\right)^{n}\)

or, \(\quad \mathrm{n}=4\)

or \(\quad \frac{t}{\mathrm{T}}=4\)

or \(\quad \mathrm{t}=4 \times \mathrm{T}=4 \times 5730=22920\) \(years\)