**Core Concept:**
Pharmacokinetic properties of a drug, including its half-life, determine how quickly and effectively it reaches steady state in the body. Steady state occurs when the drug concentration in the blood remains constant despite continuous administration, indicating that the drug has reached a balance between absorption, distribution, and elimination.

**Why the Correct Answer is Right:**
To reach 75% of steady state, we must know the drug's half-life (6 hours in this case). In a continuous intravenous infusion, the drug's concentration will increase linearly over time due to the constant influx of the drug into the body. To reach 75% of steady state, we can use the following formula:

**Formula:** (100 / drug half-life) * drug half-life

Applying this formula to our drug with a half-life of 6 hours:

(100 / 6) * 6 = 16.67 hours

Since we want to reach 75% of steady state, we need to add 33.33 hours (which is 2 half-lives) to the time it takes for the drug to reach 50% of steady state:

**Correct Answer:**
2 * 6 hours + 6 hours = 16.67 hours

**Why Each Wrong Option is Incorrect:**
A. This option is incorrect because it uses the wrong formula (drug concentration^2) and does not consider the time needed to reach 50% of steady state (16.67 hours + 33.33 hours = 49.97 hours).
B. This option is incorrect because it uses the wrong formula (drug concentration^2) and does not consider the time needed to reach 50% of steady state (16.67 hours + 33.33 hours = 49.97 hours).
C. This option is incorrect because it uses the wrong formula (drug concentration^2) and does not consider the time needed to reach 50% of steady state (16.67 hours + 33.33 hours = 49.97 hours).
D. This option is incorrect because it uses the wrong formula (drug concentration^2) and does not consider the time needed to reach 50% of steady state (16.67 hours + 33.33 hours = 49.97 hours).

**Clinical Pearls:**
1. When administering a drug by continuous infusion, the time taken to reach a certain percentage of steady state depends on the drug's half-life and not the drug concentration itself.
2. A drug's half-life is a crucial factor in determining the time needed to reach a certain percentage of steady state.
3. To reach 50% of steady state, the total time required would be 2 half-lives plus the time taken to reach the target concentration (16.67 hours + 33.33 hours = 49.97 hours).

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### Core Concept:
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