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Question

A wooden artifact from an ancient tomb contains 60% of the carbon-14 that is present in living trees. How long ago was the artifact made? (The half-life of carbon-14 is 5730 years. Round your answer to the nearest whole number.)

Answer 1

A = A₀(0.5)^t/h, where A₀ = starting amount, t = time, h = half-life

 

0.6A₀ = A₀(0.5)^t/5730                                 divide both sides by A₀

0.6 = (0.5)^t/5730                                        take natural log of both sides

ln 0.6 = ln (0.5)^t/5730                                using law of logs

ln 0.6 = (t/5730) ln (0.5)                          calculate ln

-0.51825624 ≈ (t/5730)(-0.693147181)  multiply both sides by 5730

-2969.0826 ≈ -0.693147181t                  divide both sides the right coefficient

4284.2391 ≈ t

 

The age of the sample is approximately 4284 years.

Answer 2

1271 years old