It is in minutes since the drug was administered, the concentration, C (t) in ng/ml, of a drug in a patient's (t) = 20te-0.041 a) How long does it take for the drug to reach peak concentration? What is the peak concentration? Round your answers to one decimal place. The drug reaches its peak concentration at i The peak concentration is i The concentration after 15 minutes is i ng/ml. (b) What is the concentration of the drug in the body after 15 minutes? After an hour? Round your answers to one decimal place. The concentration after 60 minutes is. minutes. ng/ml. ng/ml. c) If the minimum effective concentration is 10 ng/ml, when should the next dose be administered?
It is in minutes since the drug was administered, the concentration, C (t) in ng/ml, of a drug in a patient's (t) = 20te-0.041 a) How long does it take for the drug to reach peak concentration? What is the peak concentration? Round your answers to one decimal place. The drug reaches its peak concentration at i The peak concentration is i The concentration after 15 minutes is i ng/ml. (b) What is the concentration of the drug in the body after 15 minutes? After an hour? Round your answers to one decimal place. The concentration after 60 minutes is. minutes. ng/ml. ng/ml. c) If the minimum effective concentration is 10 ng/ml, when should the next dose be administered?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![### Question:
(a) **What is the peak concentration?**
Fill in:
The peak concentration is [ ] ng/ml.
---
(b) **What is the concentration of the drug in the body after 15 minutes? After an hour?**
Round your answers to one decimal place.
The concentration after 15 minutes is [ ] ng/ml.
The concentration after 60 minutes is [ ] ng/ml.
---
(c) **If the minimum effective concentration is 10 ng/ml, when should the next dose be administered?**
Enter your answer to the nearest 10 minutes.
The next dose should be administered in [ ] minutes.
---
### Additional Resources:
- eTextbook and Media
- [Save for Later] button to save your progress.
This set of questions helps students understand the pharmacokinetics of drug concentration over time.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb02c27fa-9cde-4c70-877a-bf210a9f7871%2Feb1ae0d2-5f39-4aa1-b7c5-ba2bdc949ae2%2Foo0unu_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Question:
(a) **What is the peak concentration?**
Fill in:
The peak concentration is [ ] ng/ml.
---
(b) **What is the concentration of the drug in the body after 15 minutes? After an hour?**
Round your answers to one decimal place.
The concentration after 15 minutes is [ ] ng/ml.
The concentration after 60 minutes is [ ] ng/ml.
---
(c) **If the minimum effective concentration is 10 ng/ml, when should the next dose be administered?**
Enter your answer to the nearest 10 minutes.
The next dose should be administered in [ ] minutes.
---
### Additional Resources:
- eTextbook and Media
- [Save for Later] button to save your progress.
This set of questions helps students understand the pharmacokinetics of drug concentration over time.
![**Pharmacokinetics Problem Set**
Consider the following scenario for understanding drug concentration in the bloodstream. If it is \( t \) minutes since the drug was administered, the concentration \( C(t) \) in ng/mL of a drug in a patient's bloodstream is given by:
\[ C(t) = 20t e^{-0.04t} \]
**Problem (a): How long does it take for the drug to reach peak concentration?**
- Calculate the time in minutes.
- **Round your answers to one decimal place.**
The peak concentration of the drug is:
\[ \_\_\_ \text{ minutes.} \]
**Problem (b): What is the concentration of the drug in the body after 15 minutes?**
- Calculate the concentration after 15 minutes.
- Calculate the concentration after 60 minutes.
- **Round your answers to one decimal place.**
The concentration after 15 minutes is:
\[ \_\_\_ \text{ ng/mL.} \]
The concentration after 60 minutes is:
\[ \_\_\_ \text{ ng/mL.} \]
**Follow-Up Question:**
If the minimum effective concentration is 10 ng/mL, when should the next dose be administered?
This exercise incorporates mathematical modeling to determine drug dosage schedules and is crucial for ensuring therapeutic effectiveness and patient safety.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb02c27fa-9cde-4c70-877a-bf210a9f7871%2Feb1ae0d2-5f39-4aa1-b7c5-ba2bdc949ae2%2Fqnbofzn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Pharmacokinetics Problem Set**
Consider the following scenario for understanding drug concentration in the bloodstream. If it is \( t \) minutes since the drug was administered, the concentration \( C(t) \) in ng/mL of a drug in a patient's bloodstream is given by:
\[ C(t) = 20t e^{-0.04t} \]
**Problem (a): How long does it take for the drug to reach peak concentration?**
- Calculate the time in minutes.
- **Round your answers to one decimal place.**
The peak concentration of the drug is:
\[ \_\_\_ \text{ minutes.} \]
**Problem (b): What is the concentration of the drug in the body after 15 minutes?**
- Calculate the concentration after 15 minutes.
- Calculate the concentration after 60 minutes.
- **Round your answers to one decimal place.**
The concentration after 15 minutes is:
\[ \_\_\_ \text{ ng/mL.} \]
The concentration after 60 minutes is:
\[ \_\_\_ \text{ ng/mL.} \]
**Follow-Up Question:**
If the minimum effective concentration is 10 ng/mL, when should the next dose be administered?
This exercise incorporates mathematical modeling to determine drug dosage schedules and is crucial for ensuring therapeutic effectiveness and patient safety.
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