By using the formula
Activity final = activity initial x e ⁽₋λ x time⁾
λ = ln(2)/ half life
and,
-ln(activity final/activity initial) = .693/8.8 days x time
-ln[(3.55x10²⁴) / (5.68x10²⁵) = .693/8.8 days x time
2.77259 = .693/8.8 days x time
2.77259 x 8.8 days = .693 x time
24.3988 = .693 x time
24.3988/.693 = time
35.2075 = time
time it will take to sample the decay is 35.2 days