Question 1002742: 6.An anthropologist finds bone that her instruments measure it as 0.177% of the amount of Carbon-14 the bones would have contained when the person was alive. How long ago did the person die?
The half life of carbon 14 is 5,730 years. Round your answer to the nearest thousand.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! P = orginal amount of carbon 14 t years ago (right when the person died)
A = current amount of carbon 14
Since "An anthropologist finds bone that her instruments measure it as 0.177% of the amount of Carbon-14 the bones would have contained when the person was alive" we know that A = 0.00177P because 0.177% = 0.00177
The half-life formula in this case is A = P*(1/2)^(t/5730)
A = P*(1/2)^(t/5730)
0.00177P = P*(1/2)^(t/5730) Plug in A = 0.00177P
0.00177 = (1/2)^(t/5730) Divide both sides by P
Ln(0.00177) = Ln((1/2)^(t/5730)) Apply natural logs to both sides
Ln(0.00177) = (t/5730)*Ln(1/2) Use the rule Ln(x^y) = y*Ln(x)
Ln(0.00177)/Ln(1/2) = t/5730 Divide both sides by Ln(1/2)
5730*Ln(0.00177)/Ln(1/2) = t Multiply both sides by 5730
t = 5730*Ln(0.00177)/Ln(1/2) Flip the equation (a = b is the same as b = a)
t = 52,383.8601165473 Use a calculator
t = 52,383.860 Rounding to the nearest thousand (3 decimal places)
The person died approximately 52,383.860 years ago
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