### Tapering off my drug dependence

I had back surgery recently and have been taking the narcotic oxycodone, which has a half-life of 3.8 hours approximately.  I have been tapering my down my dose, taking

10mg / 4 hours

10 mg / 5 hours

10 mg / 6 hours

And now I want to drop to 5 mg, but wondered with what frequency I should take it.  I'll look at the levels remaining in my system after the doses given above, so I need to solve the half-life equation 0.5 = e^(3.8k), then evaluate

10e^(4k)

10e^(5k)

10e^(6k)

I get 4.83mg, 4.03mg, 3.36mg, respectively.  So when I drop down to the 5mg tablet, I'd like to take another when I have about 3.5mg left.  Let's see when that occurs:

3.5 = 5e^(kt)

Using k from above (have you found it yet?), I get t =~2 hours.  So I'll start with that period and increase from there.