Word problem help

Question

A team of archaeologists recovered wooden artifacts believed to be 4000 years old. How much carbon-14 has been lost from the wood?

the decay rate for carbon -14 is 0.00012

I can't figure out how to put this in A formula.... Any help is appreciated!

12/4/2013 | Erica from Seattle, WA | 2 Answers | 0 Votes

Answer 1

Dear Erica,

In general

A = A₀e-^kt

where A is the amount remaining after t years, A₀ is the starting amount and k is the decay constant.

Let us rewrite this as

A/A₀ = e^-kt = e^{-[(0.00012)*(4000)]} = e^-0.48 = 0.62

I think all we can say with certainty is that, during those 4000 years, the amount of C-14 decreased to 62% of its original value, or it lost 38% of its original value (A₀).

Answer 2

N(t)=N(0)e^-kt, where k is the decay rate. I assume k=-0.00012 is measured in year^-1, so that t is in years (in fact, it is the case, I believe, since half-life time is 5730 years for C¹⁴).

Then,

N(4000)/N(0)=e^{-0.00012*4000}=e^-0.48≈0.62

So the amount of carbon-14 left at the present moment is 0.62 or 62% of its original quantity. Therefore, 38% has been lost due to decay.

Answer: 38%