posted by Mel .
if your smoke detector contains 0.10 mg of 241Am, how long will it take to decay 1.25 * 10^-2mg
I assume you mean how long will it take to decay from 0.10 mg to 1.25E-2 mg?
k = 0.693/t1/2
ln(No/N) = kt
No = 0.10 mg
N = 1.25E-2 mg
k from above.
Substitute and solve for t. You will need to look up the half life of Am241.