Question

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

Answer 1

The person died 51,788 years ago.

Step-by-step 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* e^(-\lambda t)`

`0.002 N_o=N_o* e^{-(0.00012 (year)^(-1)) t}`

`\ln[0.002 N_o]=\ln[N_o]-{(0.00012 (year)^(-1))* 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.

Answer 2

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