Answer:
12.53 % of a sample of Uranium-238 will remain after 13.4 billion years.
Explanation:
The half life of the uranium-238 =
=4.47 billion years
All the radioactive reaction are of first order kinetics. The rate constant and t half of the reaction are related as:

![k=\frac{2.303}{t}\log\frac{[A_o]}{[A]}](https://tex.z-dn.net/?f=k%3D%5Cfrac%7B2.303%7D%7Bt%7D%5Clog%5Cfrac%7B%5BA_o%5D%7D%7B%5BA%5D%7D)
where,
k = rate constant = 
t = time taken during radio decay = 4.47 billion years
= initial amount of the reactant = 
[A] = amount left left after time t.
![\log \frac{[A]}{[A_o]}=-\frac{kt}{2.303}](https://tex.z-dn.net/?f=%5Clog%20%5Cfrac%7B%5BA%5D%7D%7B%5BA_o%5D%7D%3D-%5Cfrac%7Bkt%7D%7B2.303%7D)
![\frac{[A]}{[A_o]}=0.1253=\frac{12.53}{100}=12.53\%](https://tex.z-dn.net/?f=%5Cfrac%7B%5BA%5D%7D%7B%5BA_o%5D%7D%3D0.1253%3D%5Cfrac%7B12.53%7D%7B100%7D%3D12.53%5C%25)
12.53 % of a sample of Uranium-238 will remain after 13.4 billion years.