High concentrations of carbon monoxide CO can cause coma and possible death. The time required for a person to reach a COHb level capable of causing a coma can be approximated by the quadratic model T = .0002x²-316x + 127.9, where T is the exposure time in hours necessary to reach this level and 500 ≤x≤ 800 is the amount of carbon monoxide present in the air in parts per million (ppm). a) What is the exposure time when x = 560? b) Estimate the concentration of CO necessary to produce a coma in 8 hr. What is the exposure time when x = 560? hr (Round to the nearest tenth as needed.)
High concentrations of carbon monoxide CO can cause coma and possible death. The time required for a person to reach a COHb level capable of causing a coma can be approximated by the quadratic model T = .0002x²-316x + 127.9, where T is the exposure time in hours necessary to reach this level and 500 ≤x≤ 800 is the amount of carbon monoxide present in the air in parts per million (ppm). a) What is the exposure time when x = 560? b) Estimate the concentration of CO necessary to produce a coma in 8 hr. What is the exposure time when x = 560? hr (Round to the nearest tenth as needed.)
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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![### The Effects of Carbon Monoxide and Exposure Time Calculation
High concentrations of carbon monoxide (CO) can cause coma and possible death. The time required for a person to reach a carboxyhemoglobin (COHb) level capable of causing a coma can be approximated by the quadratic model:
\[ T = 0.0002x^2 - 0.316x + 127.9 \]
Where:
- \( T \) is the exposure time in hours necessary to reach this level.
- \( x \) represents the concentration of carbon monoxide present in the air in parts per million (ppm).
For this analysis:
- \( 500 \times x \leq 800 \) is the amount of carbon monoxide present in the air in parts per million (ppm).
#### Example Problems:
1. **What is the exposure time when \( x = 560 \)?**
To find the exposure time (\( T \)) when \( x = 560 \):
\[
T = 0.0002(560)^2 - 0.316(560) + 127.9
\]
Substitute and calculate the values accordingly.
2. **Estimate the concentration of CO necessary to produce a coma in 8 hours.**
To find the concentration (\( x \)) necessary to produce a coma in 8 hours, set \( T = 8 \) and solve the quadratic equation for \( x \).
#### Graphs and Diagrams:
(No graphs or diagrams are visible within the given text.)
Use this quadratic model to understand the relationship between carbon monoxide concentration and exposure time, ensuring proper safety measures and awareness of CO levels in various environments.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fba446a50-8bb7-4794-9fc8-884b5dcd25dd%2F2de369b5-8def-4145-a03d-79b856a0257b%2Fcn9n4rx_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### The Effects of Carbon Monoxide and Exposure Time Calculation
High concentrations of carbon monoxide (CO) can cause coma and possible death. The time required for a person to reach a carboxyhemoglobin (COHb) level capable of causing a coma can be approximated by the quadratic model:
\[ T = 0.0002x^2 - 0.316x + 127.9 \]
Where:
- \( T \) is the exposure time in hours necessary to reach this level.
- \( x \) represents the concentration of carbon monoxide present in the air in parts per million (ppm).
For this analysis:
- \( 500 \times x \leq 800 \) is the amount of carbon monoxide present in the air in parts per million (ppm).
#### Example Problems:
1. **What is the exposure time when \( x = 560 \)?**
To find the exposure time (\( T \)) when \( x = 560 \):
\[
T = 0.0002(560)^2 - 0.316(560) + 127.9
\]
Substitute and calculate the values accordingly.
2. **Estimate the concentration of CO necessary to produce a coma in 8 hours.**
To find the concentration (\( x \)) necessary to produce a coma in 8 hours, set \( T = 8 \) and solve the quadratic equation for \( x \).
#### Graphs and Diagrams:
(No graphs or diagrams are visible within the given text.)
Use this quadratic model to understand the relationship between carbon monoxide concentration and exposure time, ensuring proper safety measures and awareness of CO levels in various environments.
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