The burial cloth of an Egyptian mummy is estimated to contain 58% of the carbon-14 it contained originally. How long ago was the mummy buried? (The half-life of

Question

This exercise uses the radioactive decay model.

Answer 1

The half-life of Carbon-14 is 5730 years. Since more than half remains the answer should be less than 5730 years.

 

A = A₀(0.5)^t/h

 

0.58A_{0 ⁼} A₀(0.5)^t/5730           divide both sides by A₀

0.58 = 0.5^t/5730                          take natural log of both sides

ln 0.58 = (t/5730) ln 0.5        calculate ln

-0.54 ≈ (t/5730) (-0.69)        multiply both sides by 5730

-3094.2 ≈ -0.69 t                  divide both sides by -0.69

4484.45 ≈ t

 

The mummy is approximately four thousand four hundred years old.