SOLUTION: The half-life of carbon-14 is 5700 years.Find the age of a sample at which 18% of the radioactive nuclei originally present have decayed.

Question 449906: The half-life of carbon-14 is 5700 years.Find the age of a sample at which 18% of the radioactive nuclei originally present have decayed.
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
The half-life of carbon-14 is 5700 years.Find the age of a sample at which 18% of the radioactive nuclei originally present have decayed.
.
Exponential growth/decay formula:
N = No*e^(kt)
where
N is amount after time t
No is the initial amount
k is a constant
t is time
.
Using:
The half-life of carbon-14 is 5700 years.
to find k:
Let x = initial amount
then
.5x = xe^(5700k)
.5 = e^(5700k)
ln(.5) = 5700k
ln(.5)/5700 = k
-.0001216 = k
.
Now we can answer:
Find the age of a sample at which 18% of the radioactive nuclei originally present have decayed.
x-.18x = x*e^(-.0001216t)
x(1-.18) = x*e^(-.0001216t)
x(.82) = x*e^(-.0001216t)
.82 = e^(-.0001216t)
ln(.82) = -.0001216t
ln(.82)/(-.0001216) = t
1632 years = t

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