Question

Determine the half-life of potassium if in 3460 years a 200 g sample decayed into 25 g

Answer 1

$M=m_o*\frac{1}{2}^\frac{t}{T}\\ M-mass\ aftter\ decay\\ m-initial\ mass\\ t-time\\ T-period(half-life)\\ 25=200*\frac{1}{2}^\frac{3460}{T}|:200\\ \frac{1}{8}=(\frac{1}{2})^\frac{3460}{T}\\ (\frac{1}{2})^3=(\frac{1}{2})^\frac{3460}{T}\\ 3=\frac{3460}{T}\\ T=1153\frac{1}{3}$

or easiest way
200g ----->  100g -------> 50g -----> 25g
We can that there were three decays.
1 decay ----------- x years
3 decays---------- 3460
$x=1153\frac{1}{3}$