An antibiotic QX has half-life of 6 hours and volume of distributionof 2L/Kg. what is the expected AUC after administration of a singleiv dose of 10mg/kg

To calculate the Area Under the Curve (AUC) for the antibiotic QX, we need to use the formula for AUC in pharmacokinetics, which is:

AUC = Dose / (Cl)

Where:

• Dose is the amount of drug administered, in this case 10mg/kg.
• Cl is the clearance of the drug from the body.

The clearance (Cl) can be calculated using the formula:

Cl = 0.693 * Vd / t1/2

Where:

• 0.693 is a constant related to the natural logarithm of 2 (since we're dealing with half-life).
• Vd is the volume of distribution, in this case 2L/kg.
• t1/2 is the half-life of the drug, in this case 6 hours.

First, let's calculate the clearance:

Cl = 0.693 * 2L/kg / 6 hours = 0.231 L/kg/h

Then, we can calculate the AUC:

AUC = 10mg/kg / 0.231 L/kg/h = 43.29 mg*h/L

So, the expected AUC after administration of a single IV dose of 10mg/kg of antibiotic QX is approximately 43.29 mg*h/L.