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# Word problem help

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!

### 2 Answers by Expert Tutors

William S. | Experienced scientist, mathematician and instructor - WilliamExperienced scientist, mathematician and...
4.4 4.4 (10 lesson ratings) (10)
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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).
Kirill Z. | Physics, math tutor with great knowledge and teaching skillsPhysics, math tutor with great knowledge...
4.9 4.9 (174 lesson ratings) (174)
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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.