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[ (3.55x10 ²⁴) / (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