Forming a hypothesis comes after stating the problem.
Given :
The half life of Carbon-14 ,
.
Trace amounts of Carbon-14 1/2408 remains.
To Find :
How old is the rock .
Solution :
Let , initial concentration of Carbon-14 is C .
Quantity remains ,
.
Rate constant is :

By first order equation :
![kt=-ln(\dfrac{[A_t]}{[A_o]})\\\\t=-\dfrac{ln(\dfrac{[A_t]}{[A_o]})}{k}\\\\t=-\dfrac{ln(\dfrac{[A_o]}{[A_o]\times 2408})}{1.2\times 10^{-4}}\ years\\\\t=-\dfrac{ln(\dfrac{1}{2408})}{1.2\times 10^{-4}}\ years\\\\t=64887.9\ years](https://tex.z-dn.net/?f=kt%3D-ln%28%5Cdfrac%7B%5BA_t%5D%7D%7B%5BA_o%5D%7D%29%5C%5C%5C%5Ct%3D-%5Cdfrac%7Bln%28%5Cdfrac%7B%5BA_t%5D%7D%7B%5BA_o%5D%7D%29%7D%7Bk%7D%5C%5C%5C%5Ct%3D-%5Cdfrac%7Bln%28%5Cdfrac%7B%5BA_o%5D%7D%7B%5BA_o%5D%5Ctimes%202408%7D%29%7D%7B1.2%5Ctimes%2010%5E%7B-4%7D%7D%5C%20years%5C%5C%5C%5Ct%3D-%5Cdfrac%7Bln%28%5Cdfrac%7B1%7D%7B2408%7D%29%7D%7B1.2%5Ctimes%2010%5E%7B-4%7D%7D%5C%20years%5C%5C%5C%5Ct%3D64887.9%5C%20years)
Therefore , the rock is 64887.9 years old .
Hence , this is the required solution .