Theophylline plasma conc determined 2 hours after a single iv bolus dose was 16 mg/L. Calculate theophylline conc 8 hours after administration, if theophylline half life is 6 hours
The following equation describes the relationship between two concentrations after a single iv bolus dose.
Cp2=
Cp1 e-kt
Cp1 = 16 mg/L
k = 0.693/6 hr = 0.1155 hr-1
t= the time diffrence = 6 hours
Subtitute in the equation to obtain Cp2
Cp2 = Cp1 e -kt
Cp8 hr = Cp2 hr e -k(8-2)hr
Cp
8 hr = 16 mg/L e
-0.1155 hr-1 (6) hr
Cp8 hr = 16 mg/L (0.5)
Cp8 hr = 8 mg/L
Theophylline plasma conc determined 2 hours after a single iv bolus dose was 16 mg/L. Calculate the time required for this conc to decrease to 10 mg/L, if theophylline half life is 6 hours.
The following equation describes the relationship between two concentrations after a single iv bolus dose.
Cp2=
Cp1 e-kt
Cp1 = 16 mg/L
Cp2 = 10 mg/L
k = 0.693/6 hr = 0.1155 hr-1
Substitute in the equation to obtain t
Cp2 = Cp1 e -kt
10 mg/L = 16 mg/L e -0.1155 hr-1(t) hr
ln 16mg/L
10mg/L = -0.1155 hr-1 (t)hr
-0.47 = -0.1155 hr-1 (t)hr
t = 4.07 hr
