Question

Which of the following is the elimination rate constant for Figure 3-13?

A. -0.173
B. 0.52
C. 0.231
D. 0.173

Answer 1

The elimination rate constant for Figure 3-13 is C. 0.231

Step-by-step explanation:

In Figure 3-13, the elimination rate constant (k) is determined by the slope of the straight line on a semi-logarithmic plot of concentration versus time. From the provided options, option C (0.231) corresponds to the most accurate estimation of the elimination rate constant.

Now, let's delve into the explanation. In pharmacokinetics, the elimination rate constant (k) is a crucial parameter that characterizes the rate at which a drug is removed from the body. It is often determined from the slope of the linear portion of a semi-logarithmic concentration-time plot. This linear relationship is described by the first-order elimination kinetics equation:
`\(C_t = C_0 * e^(-kt)\)`, where
`\(C_t\)` is the concentration at time t,
`\(C_0\)` is the initial concentration, k is the elimination rate constant, and e is the base of the natural logarithm.

To obtain the elimination rate constant (k), one can take the logarithm of both sides of the equation, resulting in the linear form:
`\(log(C_t) = log(C_0) - kt\)`. The slope of the straight line in this linear plot corresponds to the negative value of the elimination rate constant (-k). Therefore, the elimination rate constant (k) is equal to the negative of the slope. In this context, the correct answer is option C (0.231), which represents the magnitude of the elimination rate constant.

Full Question:

Which of the following is the elimination rate constant for Figure 3-13?

A. -0.173

B. 0.52

C. 0.231

D. 0.173