Answer: 22.59 years
Explanation:
1) The law of disintegration decay is expressed as an exponential equation:
N = No x e ^ (-kt)
Where No is the initial number of particles (atoms), k is the disintegration constant, t is the time, and N is the number of atoms remaining after time t has elapsed.
2) By substituting N = 2292, No = 3312, and t = 12 years, you obtain the value of k:
2292 = 3312 x e^(-k×12) => -12k = ln(2292/3312) = -0.6368127 => k = 0.030677
3) Now, you can use the half-time equation (you can derive it from the equation N = No x e ^(-kt) by doing N = No / 2):
t-half = ln(2)/k = ln(2)/0.030677 = 22.59 years
