Only 10% of the carbon-14 in a wooden bowl remains. How old is the bowl (rounded to the nearest hundred years)?

Question

Only 10%  of the carbon-14  in a wooden bowl remains. How old is the bowl (rounded to the nearest hundred years)?

Answer 1

The half-life of carbon 14 is 5730 years.

 

A = a₀(0.5)^t/h, where a₀ = initiate amount, t = time in years, h = half-life in years.

 

0.1a₀ = a₀(0.5)^t/5730                  divide both sides by a₀

0.1 = (0.5)^t/5730                         take natural log of both sides

ln 0.1 = (t/5730) ln 0.5              calculate log

-2.3 ≈ (t/5730)(-0.693)             multiply both sides by 5730

-13179 ≈ -0.693t                      divide both sides by -0.693

19017.3 ≈ t

 

The bowl is approximately nineteen thousand seventeen years old.