Radioactivity is studied very well by scientists that they have established a pseudo-first order reaction for this process. The working equation for this problem is:
h = ln 2/k
where
h is the half-life
k is the reaction constant
1600 = ln2/k
k = 4.33×10⁻⁴/yr
Then, we use
A = A₀e^(-kt)
A is the amount left after time t
A₀ is the original amount
t is the time
12.5 = 100e(-4.33×10⁻⁴*t)
t = 4,800 years
