The drug propanolol, which is used as an anxiolytic (relieves anxiety) has a half-life of 3.9 h. How long does it take for 80% of a dose of propanolol to be eliminated?

After 9.0 hours

Explanation:

Using the decay equation, we can write the amount of drug propanol after time t as:

(1)

where

m(t) is the mass left at time t

is the initial mass of the substance

is the decay constant

t is the time

The decay constant is related to the half-life of the substance as follows:

where is the half-life.

Here we have

So the decay constant is

We want to find the time t after which the dose is 80% of the initial dose is eliminated, so the time t after which 20% of drug is left, so

Substituting eq(1) and solving for t, we find: