If a patient was given 1000 mg of a drug {1st order kinetics} initially and after 2 hours the drug level in plasma is 500 mg, after 8 hours what will be the level in plasma?
**Core Concept**
The question is testing the concept of first-order kinetics, where the rate of drug elimination is directly proportional to the concentration of the drug in the body. In first-order kinetics, the elimination rate constant (k) is constant, and the plasma concentration of the drug decreases exponentially over time.
**Why the Correct Answer is Right**
The patient was given 1000 mg of the drug, which is then eliminated from the body according to first-order kinetics. After 2 hours, the plasma concentration is 500 mg. To find the plasma concentration after 8 hours, we need to calculate the elimination rate constant (k). We can use the equation: C(t) = C0 * e^(-kt), where C(t) is the concentration at time t, C0 is the initial concentration, e is the base of the natural logarithm, and k is the elimination rate constant. Rearranging the equation to solve for k, we get: k = -ln(C(t)/C0)/t. Plugging in the values, we get: k = -ln(500/1000)/2 = 0.3465 h^(-1). Now, we can use this value of k to find the plasma concentration after 8 hours: C(8) = 1000 * e^(-0.3465 * 8) = 1000 * e^(-2.772) = 1000 * 0.0608 = 60.8 mg.
**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because it assumes that the drug is eliminated according to zero-order kinetics, where the rate of elimination is constant and independent of the concentration of the drug.
**Option B:** This option is incorrect because it assumes that the drug is eliminated according to first-order kinetics, but the initial concentration and time points are not consistent with the given data.
**Option C:** This option is incorrect because it assumes that the drug is eliminated according to zero-order kinetics, but the elimination rate constant is not provided.
**Clinical Pearl / High-Yield Fact**
In first-order kinetics, the elimination rate constant (k) is constant and independent of the concentration of the drug. This means that the plasma concentration of the drug decreases exponentially over time, and the half-life of the drug is constant.
**Correct Answer: C. 60.8 mg.**