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You are an archeologist digging up an ancient village and you discover a 10lb cat. A careful
analysis reveals 5 x 10-13 lbs. of carbon-14. How old is the cat, and presumably the village?


Sagot :

The age of the cat and presumably the village is approximately 13657 years. .

What is Half-Life?

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:

  • The percentage of carbon in living organisms is 19.4%
  • The mass of the cat is 10 lb.

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.

Learn more about Half-Life at: https://brainly.com/question/26689704

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