Drug Name Half-life
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Acetaminophen 1-4 hours
Ibuprofen 1.8-2 hours
Loratadine 8.4 hours
Lithium 8 hours
Diphenhydramine 5.3-11.7 hours

The table above displays the half-lives of 5 common house hold drugs. The half-life (h) is the time is takes for a substance to reduce to half its initial value (A0). Half life can be used to solve for the amount (A) of a substance left after t time by using the following equation:

A=A^0⋅(12)^t/h
If Scott was administered 300 mg of Lithium, which of the following represents how much lithium, rounded to the nearest hundredth of a mg, could be left in Scott's blood stream after 12 hours?

Select one:
A. 157.23
B. 106.07
C. 212.17
D. 188.99

To make use of the given formula for amount remaining, we need to know the original amount (300 mg), the elapsed time (12 h), and the half-life of the substance of interest (8 h).

Setup

Using the given formula with the relevant values, we have ...

A = (300 mg)·(1/2)^(12/8)

Evaluation

Using a calculator to evaluate this expression, we find the amount of Lithium remaining in Scott's system after 12 hours to be ...

A ≈ 106.07 mg