How old were bones at time they were discovered?

Question

A scientist determined that the bones from a mastodon had lost 82.8% of there carbon-14. How old were the bones at the time they were discovered?

Answer 1

If 82.8% was lost, 17.2% remained.

 

A = a₀(0.5)^t/h, where a₀ = starting amount, t = time, h = half life.

 

0.172a₀ = a₀(0.5)^t/5730       divide both sides by a₀

0.172 = (0.5)^t/5730              take natural log of both sides

ln 0.172 = (t/5730) ln 0.5     calculate

-1.760 ≈ (t/5730)(-0.693)    divide both sides by -0.693

2.54 ≈ t/5730                     multiply both sides by 5730

14552.38 ≈ t

 

The bones are approximately fourteen thousand five hundred fifty-two point thirty-eight years old.

Answer 2

The formula for age using C₁₄ dating is

 

t = 5730xln(percentage of C₁₄ remaining)/(-0.693)

 

Since the mastodon has lost 82.8% of its C₁₄, it has 17.2% left.

 

t = 5730xln(.172)/(-0.693) = 14,600 years (to 3 significant digits)