Question

the isotope caesium-137 has a half life of 30 years how long will it take for the amount of this isotope in a sample of caesium to decay to 1/16th of its origional amount. thanks

amountremaining=oriinalamount(1/2)^time/timehalflife.

1/16= (1/2)^t/30
(1/2)^4= (1/2)^t/30
so t/30= 4
solve for t in years.

Another, but longer way, of solving the problem follows:
k=0.693/t_1/2
solve for k. THEN,
ln(N_o/N)=kt

where N_o = original # atoms = 16
N = # atoms at some future time = 1
k is from above.
solve for t.
You should get the same answer either way.