The isotope 206po has a half-life of 8.8 days. if you have 5.68 x 1025 atoms of this isotope, how long will it take for the sample to decay to 3.55 x 1024 atoms

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