An anthropologist finds there is so little Carbon-14 remaining in a prehistoric bone that instruments cannot measure it. This means there is less than 0.2% of the amount of Carbon-14 the bones would have contained when the person was alive. How long ago did the person die? (The constant for Carbon-14 is 0.00012.)

Answer

13,411 years

22,491 years

45,020 years

51,788 years

So here is how we will know how long the person died.
N = Ie^(-kt)

N = Ie^(-0.00012t)

0.002I = I*e^(-0.00012t)

0.002 = e^(-0.00012t)

ln(0.002) = -0.00012t
ln(0.002)/(-0.00012) = t

51788.4008 = t

t = 51788.4008

round it off to 51,788 years
So the correct answer for this question would be the last option, option D.
Hope this answer helps.
Let me know if you need more help next time!

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Tringa0 Tringa0 · Answer 2 · 2019-07-01T02:45:20-04:00

Answer:

The person died 51,788 years ago.

Explanation:

Let the initial amount of carbon-14 in the body when person was alive =\(N_o\)

Amount of carbon-14 left after t years = \(N=0.2\% of N_o=0.002 N_o\)

t = time elapsed

Decay constant of carbon-14=\(\lambda =0.00012 (year)^{-1}\)

\(N=N_o\times e^{-\lambda t}\)

\(0.002 N_o=N_o\times e^{-(0.00012 (year)^{-1}) t}\)

\(\ln[0.002 N_o]=\ln[N_o]-{(0.00012 (year)^{-1})\times t\)

t = 51,788.40 years ≈ 51,788 years

Since the carbon-14 in less than 0.02 % in the body which means the person must have died 51,788 years ago.