Okay, let's tackle this pharmacokinetics question. The patient has severe asthma and is receiving theophylline via IV infusion. The question is asking how long it takes to reach 93.75% of the steady-state concentration.

First, I need to recall the concept of steady-state in pharmacokinetics. Steady-state is achieved when the rate of drug administration equals the rate of elimination. For IV infusions, the time to reach steady-state depends on the drug's half-life.

The half-life given is 8 hours. I remember that each half-life, the drug accumulates by about 50% of the remaining distance to steady-state. So after one half-life (8 hours), it's 50%, then 75% after two, 87.5% after three, and 93.75% after four half-lives. Wait, 93.75% is four half-lives because each half-life adds 50% of the remaining. Let me verify: 1st half-life: 50%, 2nd: 50% of 50% left = 25% added (total 75%), 3rd: 12.5% (total 87.5%), 4th: 6.25% (total 93.75%). Yes, that's right. So four half-lives would be 4 x 8 hours = 32 hours.

The options probably include 32 hours as one of the choices. The question is structured to test understanding of how half-lives relate to time to reach steady-state. The other parameters given (Vd and CL) might be distractors since they aren't needed for this calculation.

Let me check if there's any other way to approach this. The formula for time to reach steady-state is t = (4 × t₁/₂), which is a standard approximation. The 93.75% is a classic 4 half-lives value. So the answer should be 32 hours. The other options might be 8, 16, 24, or 40 hours. The key here is knowing that 93.75% corresponds to four half-lives regardless of the infusion rate, as long as the infusion is continuous. The infusion rate (0.48 mg/min) isn't needed here because the time to steady-state is independent of the infusion rate or the drug's volume of distribution and clearance. It's purely dependent on the half-life.

So, the correct answer is four half-lives, which is 4 × 8 = 32 hours. The distractors would be other multiples, but the key is the 93.75% which is a standard value for four half-lives.

**Core Concept**
The time to reach steady-state concentration during a continuous intravenous infusion depends solely on the drug's half-life. Each half-life allows the drug to accumulate 50% of the remaining distance toward steady-state, with 93.75% achieved after four half-lives.

**Why the Correct Answer is Right**
Theophylline's half-life is 8 hours. To reach 93.75% of steady-state, it takes **four half

✓ Correct Answer: D. Approximately 32hrs