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The age of the cat and presumably the village is approximately 13657 years. .
Half-Life is the time taken for half the amount of a substance to disappear.
To determine the age of the cat fossil, the following should be noted:
Mass of carbon in the sample = 0.194 × 10 lb = 1.94 lb
Ratio of carbon-12 to carbon-14 = 1 : 1.35 × 10^-12
Mass of carbon-14 initially present = 1.94 × 1/1.35 × 10^-12 = 2.619 × 10^-12
Ratio of present and original mass of carbon-14 = (5 × 10-13)/2.619 × 10^-12 =
The half-life of carbon-14 = 5700 years
The ratio of the mass of carbon-14 at present and initially = 0.191
Using the half-life formula, to calculate time elapsed:
[tex]t = \frac{t_{\frac{1}{2}}ln\frac{N_t}{N_o}}{-0.693}[/tex]
Substituting the values to solve for time, t, in years
[tex]t = \frac{5700 \times \: ln(0.191) }{-0.693} = 13656.8[/tex]
Time elapsed, t = 13656.8 years.
Therefore, the age of the cat and presumably the village is approximately 13657 years.
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