Answer:
The mammoth bone is 22726 years old.
Explanation:
We can find how hold is the mammoth bone using the decay equation:
[tex]N(t) = N_{0}*e^{-\lambda t}[/tex] (1)
Where:
N(t): is the quantity at time t = 6.25%N₀
N₀: is the initial quantity
λ: is the decay constant
First, we need to find λ:
[tex] \lambda = \frac{ln(2)}{t_{1/2}} = \frac{ln(2)}{5700 y} = 1.22 \cdot 10^{-4} y [/tex]
Now, by solving equation (1) for t we have:
[tex]t = \frac{ln(\frac{N(t)}{N_{0}})}{-\lambda} = \frac{ln(0.0625)}{-1.22 \cdot 10^{-4}} = 22726 y[/tex]
Therefore, the mammoth bone is 22726 years old.
I hope it helps you!
