Answer:
n = A / A0 where n is the fraction of the sample remaining
If T is the half-life then
A = T^n * A0 = (1/2)^n A0
This is easy if A / A0 = 1/2, 1/4, 1/8, or 1/16 = 1/2*n where n is integral
Otherwise,
ln (A / A0) = -n ln 2 = -.693 n
Suppose 1000 = amt remaining and 10000 was initially present
Then ln A / A0 = .1 (more than 3 but less than 4 half-lives)
n = -ln .1 / .693 = 3.32
n^3.32 = .1 where n is the number of half=lives