Mathematical Expressions

b- If you know the elimination rate constant and the amount of drug at a specific time after drug administration, you can calculate the amount of drug in the body at any time afterward.

InA2 = InA1-kt
log A2 = log A1 -

kt

2.303
A2 = A1e-kt
You can substitute for the
values of A1, k and t in
any of these equations to
calculate A2 at any time.
A1

Example:


After administration of an iv dose of theophylline the amount of theophylline remaining in the body after 3 hours was 250 mg. What will be the theophylline amount remaining in the body after 8 hours if the elimination rate constant of theophylline in this patient is 0.183 hr -1 ?


A2 = A1 e-kt
A8hr = A3hr e-k(8-3)hr
A8hr = 250mg e-01.83hr-1(5hr)
A8hr = 250mg (0.4)
A8hr = 100 mg
You can substitute for the
value of A1, k and t in any of these equations to
calculate the amount
remaining (A2) after 8 hours.
A1 = 250 mg
A2 = ?
t1 = 3 hr
t2 = 8 hr
k = 0.183 hr -1
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