2000 1800 1600 1400 1200 (1, 1200) 1000 800 600 (3, 600) 400 200 3 6. Time (hours) (a) What is the average rate of change (in bacteria per hour) of the number of bacteria in the culture between 1 and 3 hours after the measurements begin? (E -250 x bacteria per hour (b) Write a sentence that explains the meaning of the average rate of change in the context of this exercise. (Fill in the blanks. There are two answer blanks. A Because the average rate of change is the bacteria population is decreasing at an average rate of bacteria per hour between 1 and 3 hours af first blank O positive O negative second blank (Enter an exact number.) Number of Bacteria

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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The following section details the decrease in the number of bacteria in a culture over time, represented by a graph.

### Graph Description

- **Graph Title:** Number of Bacteria over Time
- **Axes:**
  - Horizontal Axis (x-axis): Time (hours) ranging from 0 to 6.
  - Vertical Axis (y-axis): Number of Bacteria ranging from 0 to 2000.
- **Data Points:**
  - Two key points are marked: 
    - At 1 hour: 1200 bacteria
    - At 3 hours: 600 bacteria
- **Curve:** The curve on the graph shows a declining trend in the number of bacteria over time.

### Questions and Answers

**(a)** What is the average rate of change (in bacteria per hour) of the number of bacteria in the culture between 1 and 3 hours after the measurements begin?

- **Answer:** The average rate of change is -300 bacteria per hour.

**(b)** Write a sentence that explains the meaning of the average rate of change in this context. (Fill in the blanks. There are two answer blanks.)

- **Sentence:** Because the average rate of change is negative, the bacteria population is decreasing at an average rate of 300 bacteria per hour between 1 and 3 hours after the measurements begin.
Transcribed Image Text:The following section details the decrease in the number of bacteria in a culture over time, represented by a graph. ### Graph Description - **Graph Title:** Number of Bacteria over Time - **Axes:** - Horizontal Axis (x-axis): Time (hours) ranging from 0 to 6. - Vertical Axis (y-axis): Number of Bacteria ranging from 0 to 2000. - **Data Points:** - Two key points are marked: - At 1 hour: 1200 bacteria - At 3 hours: 600 bacteria - **Curve:** The curve on the graph shows a declining trend in the number of bacteria over time. ### Questions and Answers **(a)** What is the average rate of change (in bacteria per hour) of the number of bacteria in the culture between 1 and 3 hours after the measurements begin? - **Answer:** The average rate of change is -300 bacteria per hour. **(b)** Write a sentence that explains the meaning of the average rate of change in this context. (Fill in the blanks. There are two answer blanks.) - **Sentence:** Because the average rate of change is negative, the bacteria population is decreasing at an average rate of 300 bacteria per hour between 1 and 3 hours after the measurements begin.
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