Answer:
17190 years
Explanation:
The exponential decay equation is:
[tex] N_{t} = N_{0}e^{-\lambda t} [/tex]
[tex] \frac{N_{t}}{N_{0}} = e^{-\lambda t} [/tex]
Where:
N(t) is the quantity at time t
N₀ is the initial amount
λ is the decay constant = ln(2)/t(1/2)
t(1/2) is the half-life
Since the ratio of carbon-14 to carbon-12 is 12.5%, we have that:
[tex] \frac{N_{t}}{N_{0}} = e^{-\lambda t} [/tex]
[tex] \frac{0.125N_{0}}{N_{0}} = e^{-\lambda t} [/tex]
[tex] ln(0.125) = -\lambda t [/tex]
By solving the above equation for t:
[tex] t = \frac{ln(0.125)}{-\lambda} = \frac{ln(0.125)}{-ln(2)/t_{1/2}} = \frac{5730 y* ln(0.125)}{-ln(2)} = 17190 y [/tex]
Therefore, the site is 17190 years old.
I hope it helps you!
