Answer:
The age of the bones is approximately 14172 years.
Explanation:
The age of the bones can be determinated using the following decay equation:
[tex] N_{(t)} = N_{0}e^{-\lambda t} [/tex] (1)
Where:
N(t): is the quantity of C-14 at time t
No: is the initial quantity of C-14
λ: is the decay rate
t: is the time
First, we need to find λ:
[tex] \lambda = \frac{ln(2)}{t_{1/2}} [/tex]
Where:
t(1/2): is the half-life of C-14 = 5730 y
[tex] \lambda = \frac{ln(2)}{5730 y} = 1.21 \cdot 10^{-04} y^{-1} [/tex]
Now, we can calculate the age of the bones by solving equation (1) for t:
[tex] t = \frac{-ln(\frac{N_{(t)}}{N_{0}})}{\lambda} [/tex]
We know that the bones have lost 82% of the C-14 they originally contained, so:
[tex]N_{t} = (1 - 0.82)N_{0} = 0.18N_{0}[/tex]
[tex]t = \frac{-ln(0.18)}{1.21 \cdot 10^{-04} y^{-1}}[/tex]
[tex]t = 14172 y[/tex]
Therefore, the age of the bones is approximately 14172 years.
I hope it helps you!
