The answer is 141 years old.
It can be calculated using the equation: (1/2)ⁿ = x
x - decimal amount remaining,
n - number of half-lives.
x = 12.5% = 12.5%/100% = 0.125
n = ?
(1/2)ⁿ = 0.125
log((1/2)ⁿ) = log(0.125)
n * log(1/2) = log(0.125)
n = log(0.125)/log(1/2) = log(0.125)/log(0.50) = -0.903 / -0.301 = 3
Number of half-lives is 3.
Number of half-lives (n) is quotient of total time elapsed (t) and length of half-life (H).
n = t/H
t = n * H
n = 3
H = 47 years
t = 3 * 47 years = 141 years
