The drug concentration in the bloodstream t hours after injection is given approximately byC(t)=5.45e−t, 0≤t≤5,where C(t) is the concentration in milligrams per milliliter.(A) What is the rate of change of concentration after 1 hour? After 4 hours?(B) Graph the function C(t)=5.45e−t The image presents a problem related to the concentration of a drug in the bloodstream over time.**Problem Statement:**The drug concentration in the bloodstream $ t $ hours after injection is given by the function $ C(t) = 5.4e^{-t} $ for $ 0 \leq t \leq 5 $, where $ C(t) $ is the concentration in milligrams per milliliter.**Questions:**1. **(A)** What is the rate of change of concentration after 1 hour? Round to three decimal places if necessary.2. **(B) Graph C.** - Select the correct graph from the options below.**Answers:****(A)** Select the correct choice below and fill in the answer box to complete your choice: - $ A: $ After 1 hour, the concentration is increasing at the rate of $\mathbf{-2.00}$ mg/mL per hour. - $ B: $ After 1 hour, the concentration is decreasing at the rate of $\mathbf{-2.00}$ mg/mL per hour. - $ C: $ After 1 hour, the rate is neither increasing nor decreasing.**Select the correct choice:** - $ A: $ After 1 hour, the concentration is increasing at the rate of $\mathbf{-5.906}$ mg/mL per hour. - $ B: $ After 1 hour, the concentration is decreasing at the rate of $\mathbf{-5.906}$ mg/mL per hour. - $ C: $ After 1 hour, the rate is neither increasing nor decreasing.**(B) Graph C****Choose the correct graph below:** - $ A: $ (No image of graph A is shown) - $ B: $ (No image of graph B is shown) - $ C: $ (No image of graph C is shown)(Note: The text does not include diagrams or graphs to detail; it instructs to choose from provided graph options that are not visible in this transcription.) **Educational Text Transcription and Explanation:**---**(B) Graph C**1. $\_\_$ After 4 hours, the rate is neither increasing nor decreasing.Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round until the final answer. Then, round to the nearest hundredth as needed.)- $\bigcirc$ A. After 4 hours, the concentration is increasing at a rate of $\_\_\_\_$\% per hour.- $\bigcirc$ B. After 4 hours, the concentration is decreasing at a rate of $\_\_\_\_$\% per hour.- $\bigcirc$ C. After 4 hours, the rate is neither increasing nor decreasing.**(B) Graph the function C(t) = 5.64t.**Choose the correct graph below:- $\bigcirc$ A. ![Graph A](#)- $\bigcirc$ B. ![Graph B](#)- $\bigcirc$ C. ![Graph C](#)- $\bigcirc$ D. ![Graph D](#)**Explanation of Graphs:**- **Graph A**: A line graph that appears to show a linear increase. The x-axis represents time, while the y-axis represents concentration. - **Graph B**: A graph displaying a curve that increases at an increasing rate, indicative of exponential growth. This suggests the function significantly grows as time increases.- **Graph C**: This graph presents a steady, linear increase, suggesting a direct proportionality between time and concentration without significant fluctuations. - **Graph D**: Features a curve that starts steep and levels off, indicating an initial rapid increase that slows over time.---This transcription and explanation are designed to support understanding of mathematical concepts related to rates and graph interpretation in an educational setting.

Answered: Image /qna-images/answer/c1ed6b13-1e73-492a-a447-4ce1e72be4f8.jpg

The drug concentration in the bloodstreams t hours after injection en mately by C-5.450s155, where is the conce (A) What is the rate of change of concentration after 1 hour? Afer 4 tour? (B) Graph C (A) Select the correct choice below and it in the awer box to complete your choke (Type an integer or a decimal. Do not round und the final am OA After 1 hour, the concentration is increasing at the rate of OR After 1 hour the concentration is decreasing at the rate of OC. After 1 hour, the rate is neither increasing nor decreasing Select the corect choice below and s (Type an integer or a decitual. Do not Thon round to the nearest hundred as needed) er box to complete your choice law OBL per hour min per hour OA. After 4bours the concentration is increasing at the rate OB. After 4 hours, the concentration is decreasing at the rate of OC. After &burs, the rate in neither increasing nor decreasing () Oraph the function C)545 Choose the correct graph below OA Thin round to the nearest hundredh as needed) mg per hour mini per hou OC OD o in milligrams per n

The drug concentration in the bloodstreams t hours after injection en mately by C-5.450s155, where is the conce (A) What is the rate of change of concentration after 1 hour? Afer 4 tour? (B) Graph C (A) Select the correct choice below and it in the awer box to complete your choke (Type an integer or a decimal. Do not round und the final am OA After 1 hour, the concentration is increasing at the rate of OR After 1 hour the concentration is decreasing at the rate of OC. After 1 hour, the rate is neither increasing nor decreasing Select the corect choice below and s (Type an integer or a decitual. Do not Thon round to the nearest hundred as needed) er box to complete your choice law OBL per hour min per hour OA. After 4bours the concentration is increasing at the rate OB. After 4 hours, the concentration is decreasing at the rate of OC. After &burs, the rate in neither increasing nor decreasing () Oraph the function C)545 Choose the correct graph below OA Thin round to the nearest hundredh as needed) mg per hour mini per hou OC OD o in milligrams per n

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

The drug concentration in the bloodstream t hours after injection is given approximately by

C(t)=5.45e^−t, 0≤t≤5,

where C(t) is the concentration in milligrams per milliliter.

(A) What is the rate of change of concentration after 1 hour? After 4 hours?

(B) Graph the function C(t)=5.45e^−t

The image presents a problem related to the concentration of a drug in the bloodstream over time.

**Problem Statement:**
The drug concentration in the bloodstream $ t $ hours after injection is given by the function $ C(t) = 5.4e^{-t} $ for $ 0 \leq t \leq 5 $, where $ C(t) $ is the concentration in milligrams per milliliter.

**Questions:**

1. **(A)** What is the rate of change of concentration after 1 hour? Round to three decimal places if necessary.

2. **(B) Graph C.**
- Select the correct graph from the options below.

**Answers:**

**(A)** Select the correct choice below and fill in the answer box to complete your choice:
- $ A: $ After 1 hour, the concentration is increasing at the rate of $\mathbf{-2.00}$ mg/mL per hour.
- $ B: $ After 1 hour, the concentration is decreasing at the rate of $\mathbf{-2.00}$ mg/mL per hour.
- $ C: $ After 1 hour, the rate is neither increasing nor decreasing.

**Select the correct choice:**
- $ A: $ After 1 hour, the concentration is increasing at the rate of $\mathbf{-5.906}$ mg/mL per hour.
- $ B: $ After 1 hour, the concentration is decreasing at the rate of $\mathbf{-5.906}$ mg/mL per hour.
- $ C: $ After 1 hour, the rate is neither increasing nor decreasing.

**(B) Graph C**

**Choose the correct graph below:**
- $ A: $ (No image of graph A is shown)
- $ B: $ (No image of graph B is shown)
- $ C: $ (No image of graph C is shown)

(Note: The text does not include diagrams or graphs to detail; it instructs to choose from provided graph options that are not visible in this transcription.)

**Educational Text Transcription and Explanation:**

---

**(B) Graph C**

1. $\_\_$ After 4 hours, the rate is neither increasing nor decreasing.

Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round until the final answer. Then, round to the nearest hundredth as needed.)

- $\bigcirc$ A. After 4 hours, the concentration is increasing at a rate of $\_\_\_\_$\% per hour.
- $\bigcirc$ B. After 4 hours, the concentration is decreasing at a rate of $\_\_\_\_$\% per hour.
- $\bigcirc$ C. After 4 hours, the rate is neither increasing nor decreasing.

**(B) Graph the function C(t) = 5.64t.**

Choose the correct graph below:

- $\bigcirc$ A. ![Graph A](#)
- $\bigcirc$ B. ![Graph B](#)
- $\bigcirc$ C. ![Graph C](#)
- $\bigcirc$ D. ![Graph D](#)

**Explanation of Graphs:**

- **Graph A**: A line graph that appears to show a linear increase. The x-axis represents time, while the y-axis represents concentration.

- **Graph B**: A graph displaying a curve that increases at an increasing rate, indicative of exponential growth. This suggests the function significantly grows as time increases.

- **Graph C**: This graph presents a steady, linear increase, suggesting a direct proportionality between time and concentration without significant fluctuations.

- **Graph D**: Features a curve that starts steep and levels off, indicating an initial rapid increase that slows over time.

---

This transcription and explanation are designed to support understanding of mathematical concepts related to rates and graph interpretation in an educational setting.

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