Answer:
The bones are 16925 years old
Explanation:
We have to use the radioactive decay law and know that the half life of carbon-14 is [tex]t_{\frac{1}{2}}=5730 \, years[/tex]. From this information we can know the decay rate of the carbon 14,
[tex]\lambda=\frac{ln(2)}{t_{\frac{1}{2}}}=1.21\times 10^{-4} s^{-1}[/tex]
Now to know the age of the bones we must directly use the radioactive decay law:
[tex]N(t)=N_0e^{-\lambda t}=0.129N_0[/tex]
Where the rightmost part of the equation comes from the statement that the activity found is just 12.9% of the activity that would be found in a similar live animal. This means that the number of carbon-14 atoms is just 12.9% of what it was at the moment the saber-toothed tiger died.
Solving for t we have:
[tex]t=-\frac{ln(0.129)}{\lambda}=16925 \, years[/tex]
