The seashell is 28747.96 years old.
Why?
If we need to calculate how old is something, we can use the equation for radioactive decay rate. It's possible using the C-14 half-life (5740 years) as reference. Remember, C-14 is used because all the living things take up the element from the atmosphere, when an organism dies, the amount of carbon starts to decay (very slowly).
Decay rate half life:
[tex]N_{t}=N_{o}*e^{-l*t}[/tex]
Where,
[tex]N_o}[/tex] is the initial number of atoms (undecayed)
[tex]N_{t}[/tex] is the the number of atoms at time (undecayed)
[tex]l[/tex] is the decay rate
Now, isolating the decay rate of the formula, we have:
{[tex]N_{t}=N_{o}*e^{-l*t}\\\\ln(\frac{N_{t}}{N_{o}})=-l*t\\[/tex]
Also, we can get the value of the decay rate (half life), using the following formula:
[tex]l=\frac{0.693}{5740}=1.207x10^{-4}[/tex]
Then, using the given information, we have:
[tex]ln(\frac{3.1}{100})=-1.207x10^{-4}*t[/tex]
[tex]-3.47=-1.207x10^{-4}*t[/tex]
[tex]-3.47=-1.207x10^{-4}*t\\\\t=\frac{-3.47}{1.207x10^{-4}}=28748.96years[/tex]
Hence, the seashell is 28748.96 years old.
Have a nice day!
