High concentrations of carbon monoxide CO can cause coma and

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 2 can be approximated by the quadratic model T = .0002x^2 - .316x + 127.9, where T is the exposure time in hours necessary to reach this level and 500 lessthanorequalto x lessthanorequalto 800 is the amount of carbon monoxide present in the air in parts per million (ppm). What is the exposure time when x = 540? Estimate the concentration of CO necessary to produce a coma in 7 hr. What is the exposure time when x = 540? (Round to the nearest tenth as needed.) Estimate the approximate concentration of CO necessary to produce a coma in 7 hr. (Round to the nearest tenth as needed.)

Solution

a) When x = 540, T = 0.0002(540)² – 0.316(540)+ 127.9 = 0.0002(291600) – 0.316(540)+ 127.9 = 58.32 – 170.64 + 127.9 = 15.58 hours = 15.6 ( on rounding off to the nearest tenth).Thus, the required exposure time is 15.58 hours = 15.6.

b) When T = 7, we have 7 = 0.0002x² – 0.316x + 127.9 or, 0.0002x² – 0.316x + 120.9 = 0On multiplying by 10000, we get 2x² – 3160x + 1209000 = 0. Therefore, x = [ -( -3160) ± { ( -3160)² – 4*2*1209000} ]/2*2 = [ 3160 ± ( 9985600- 9672000) ] /4 = (3160± 313600)/4 = (3160± 560)/4 Thus, either x = (3160- 560)/4 = 2600/4 = 650 or, x = (3160+ 560)/4 = 3720/4 = 930. Since 500 x 800, we have x = 650. Thus, the required concentration level is 650 ppm.