Question

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 Tequals=.0002xsquared2minus−.316xplus+​127.9, where T is the exposure time in hours necessary to reach this level and 500less than or equals≤xless than or equals≤800 is the amount of carbon monoxide present in the air in parts per million​ (ppm).

​a) What is the exposure time when xequals=540540​?
​b) Estimate the concentration of CO necessary to produce a coma in 99 hr.

Answer 1

T=.0002x^2 - .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).
Estimate the approximate concentration of (CO) necessary to produce a coma in
4 hrs
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4 = 0.0002x^2 - .316x + 127.9
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0.0002x^2 - .316x + 123.9 = 0
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Solve using the Quadratic Formula:
x = [0.316 +- sqrt(0.316^2 - 4*0.0002*123.9)]/[2(0.0002)]
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x = [0.316 +- sqrt(0.0007360]/0.0004
x = [0.316+-0.027129]/0.0004
x = 857.82 ppm or x = 722.18 ppm