The half-life of cesium-137 is 30 years. suppose we have a 200-mg sample.

a) To find the mass after t years:

we will use this formula:

A = Ao / 2^n

when A = the amount remaining

and Ao = the initial amount

and n = t / t (1/2)

by substitution:

∴ A = 200 mg / 2^ (t/30y)

b) Mass after 90 y:

by using the previous formula and substitute t by 90 y

A = 200mg / 2^ (90y/30y)

∴ A = 25 mg

C) Time for 1 mg remaining:

when A = Ao / 2^ (t/t (1/2)

so, by substitution:

1 mg = 200 mg / 2^ (t/30y)

∴2^ (t/30y) = 200 mg by solving for t

∴ t = 229 y