Determining The Half-Life Of Drug B Discussion Paper

## Question

Time 10:15 AM Concentration 17.3 mg/L

Time 4:30 PM Concentration 4.1 mg/L

The half-life is:

**a. 3.2 hrs**

**b. 7 hrs**

**c. 11.51 hrs**

**d. 2.05 hrs**

**e. 3.01 hrs
**

## Expert Answer

This solution was written by a subject matter expert. It’s designed to help students like you learn core concepts. Determining The Half-Life Of Drug B Discussion Paper

### Step-by-step

1st step

All steps

Answer only

Step 1/2

**ANSWER:-**

To determine the half-life of Drug B, we can use the following formula:

t1/2 = (0.693 x t) / log(C1/C2)

Where t is the time between the two concentrations, C1 is the concentration at the first time point, and C2 is the concentration at the second time point.

Using the given data:

t = 6 hours and 15 minutes = 6.25 hours

C1 = 17.3 mg/L

C2 = 4.1 mg/L

Plugging these values into the formula:

t1/2 = (0.693 x 6.25) / log(17.3/4.1) = 11.51 hours

**Therefore, the half-life of Drug B is c. 11.51 hrs.**Explanation:

- To determine the half-life of a drug, we need to measure the concentration of the drug at two different time points. The time between these two measurements is denoted by t. The half-life is the time it takes for the drug concentration to decrease by half.
- In this case, we have two measurements of Drug B concentration, one at 10:15 AM and the other at 4:30 PM. The time between these two measurements is 6 hours and 15 minutes, or 6.25 hours.
- Using the formula t1/2 = (0.693 x t) / log(C1/C2), we can calculate the half-life of Drug B. The formula uses the natural logarithm of the ratio of the concentrations at the two time points to calculate the half-life.
- Plugging in the values from the given data, we get:
- t1/2 = (0.693 x 6.25) / log(17.3/4.1)
- Simplifying this expression, we get:
- t1/2 = 11.51 hours

Therefore, the half-life of Drug B is approximately 11.51 hours.

Step 2/2

**EXAMPLE FOR PRACTICE AND FOR BETTER UNDERSTANDING**Here’s an example problem:

A patient is receiving a continuous infusion of Drug A at a rate of 50 mg/hr. The initial concentration of Drug A is 10 mg/L. If the half-life of Drug A is 3 hours, what will be the concentration of the drug in the patient’s bloodstream after 6 hours of continuous infusion?

To solve this problem, we can use the following formula:

C = Co x e^(-kt)

Where C is the concentration of the drug at time t, Co is the initial concentration of the drug, k is the elimination rate constant, and t is the time.

The elimination rate constant is related to the half-life of the drug as follows:

k = 0.693 / t1/2

Plugging in the values from the problem, we get:

k = 0.693 / 3 = 0.231

Now we can use the formula C = Co x e^(-kt) to find the concentration of Drug A after 6 hours of continuous infusion:

C = 10 x e^(-0.231 x 6) = 3.43 mg/L

Therefore, after 6 hours of continuous infusion, the concentration of Drug A in the patient’s bloodstream will be approximately 3.43 mg/L.

Explanation:

- This problem involves calculating the concentration of Drug A in the patient’s bloodstream after 6 hours of continuous infusion, given the initial concentration of the drug, the infusion rate, and the drug’s half-life.
- To solve this problem, we first need to determine the elimination rate constant, k, using the half-life of the drug. The elimination rate constant is a measure of how quickly the drug is being cleared from the body. It is related to the half-life of the drug by the following formula:
- k = 0.693 / t1/2
- Plugging in the given half-life of 3 hours, we get:
- k = 0.693 / 3 = 0.231
- Next, we can use the formula for exponential decay of drug concentration over time to calculate the concentration of Drug A in the patient’s bloodstream after 6 hours of continuous infusion. The formula is:
- C = Co x e^(-kt)
- where C is the concentration of the drug at time t, Co is the initial concentration of the drug, k is the elimination rate constant, and t is the time.
- Plugging in the given values for Co, k, and t, we get:
- C = 10 x e^(-0.231 x 6) = 3.43 mg/L

Therefore, after 6 hours of continuous infusion, the concentration of Drug A in the patient’s bloodstream will be approximately 3.43 mg/L.

Final answer

The half-life of Drug B is

**c. 11.51 hrs.**

**I hope my explanation was clear and helpful!**

**PLEASE DO LIKE**

**THANKS**Determining The Half-Life Of Drug B Discussion Paper