Iodine-125 (125I) is used to treat, among other things, brain tumors and prostate cancer. It decays by gamma decay with a half-life of 54.90 days....

Half life is the amount of time after which only 50% of the original quantity remains. For example, the half life of Iodine-125 is 54.9 days. This means that after 54.9 days, half of the original implant value would have decayed. Similarly, after 2 half lives or 109.8 days (= 2 x 54.9 days), only 25% of the original content would be left. 

The initial decay rate or activity (A0) = 532 `mu`Ci, time period = 389 days.

Decay constant, `lambda`  = 0.693/T, where T = half life = 54.9 days

Using `A = A_0 e^(-lambdat)`

Solving for a time duration, t = 389 days, we get A = 3.92 `mu`Ci

For 16.5% of the initial value, A = 16.5% of A0 = 0.165 A0

Substituting this into the equation, we get

`A/A_0 = e^(-lambdat) = 0.165`

substituting the value of decay constant, we get, t = 142.74 days.

Assuming there are 30 days in a month, it will take about 4.76 months for the activity to be 16.5% of the initial value.

Hope this helps.