Can't get the answer to this.

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 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).

 

a) What is the exposure time when x= 600? _____hr

b) Estimate the concentration of CO necessary to produce a coma in 9 hr.

 

Answer 1

a)  Substitute 600 in place of x in the equation.  T = .0002(600)²-.316(600) + 127.9 = 10.3 Hours

 

b)  You are trying to solve the equation .0002x² -.316x + 127.9 = 9.  You can use a graphing calculator and put the left side equation into Y1 and the right side into Y2 and find their intersection or you can use the quadratic formula to solve this equation.  

 

First set the equation = to 0 by subtracting 9 from both sides. .0002x² -.316x + 118.9=0.  Then substitue into

x = -b ±√(b²-4ac) all divided by 2a.  

x =( .316±√((-.316)²-4(.0002)(118.9))) / 2(.0002) 

x =(.316 ± √.004736) .0004

x =(.316 ± .0688186021)/.0004

x =(.316 + .0688186021)/.0004 or x=(.316-.0688186021)/.0004

x = 962.05 which is not within the domain of x or x = 617.95 which is within the domain of x.  Therefore 617.95 is the correct answer.