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anonymous
 one year ago
Carbon dioxide at high enough concentrations is lethal. According to the EPA (
http://www.epa.gov/ozone/snap/fire/co2/co2report.html),
exposure to ambient air concentrations greater than 17 % can cause death within one minute. Recall that we constructed the following model for gas exchange in the human lung:
ct+1=(1−q)ct+qγ,
where q is the fraction of air in the lung that is exchanged for ambient air at each breath, γ is the concentration of chemical in the ambient air, and ct is the concentration of chemical in the lung.
anonymous
 one year ago
Carbon dioxide at high enough concentrations is lethal. According to the EPA ( http://www.epa.gov/ozone/snap/fire/co2/co2report.html), exposure to ambient air concentrations greater than 17 % can cause death within one minute. Recall that we constructed the following model for gas exchange in the human lung: ct+1=(1−q)ct+qγ, where q is the fraction of air in the lung that is exchanged for ambient air at each breath, γ is the concentration of chemical in the ambient air, and ct is the concentration of chemical in the lung.

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Suppose that the ambient air has a CO2 concentration of 20 % (a concentration sufficient for fire suppression), and that a fire fighter whose oxygen mask has failed is exposed to this air. Suppose that the fire fighter has no CO2 in his lungs and that he exchanges 30 % of the air in his lungs for ambient air at every breath. In the following, you can use γ=0.2 (so that ct is measured as the fraction of the air that is CO2).

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Now suppose that the fraction of gas exchanged at each breath is only 10 %. What is the concentration in the lung after 4 breaths? so c4 = ? this is where I am stuck!!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0First off, is this your formula? \[C_t+1=(1q)C_t+q \gamma\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0thank you for responding!! :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I found equilibrium which is C^* = 0.2

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\(q\) is the fraction of air in the lung that is exchanged for ambient air at each breath = 0.3 \(\gamma\) is the concentration of chemical in the ambient air = 0.2 \(C_t\) is the concentration of chemical in the lung = what we're looking for where does the 10% come in?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0sorry I'm just laying it all out, trying to understand the question

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the 10% is the next part of the question, so I think they are saying now the fraction of gas exchanged at each breath is only 10 %, whereas before I think it was 20%

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0No not 20%, it was 30% originally

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0"in his lungs and that he exchanges 30 % of the air in his lungs for ambient air at every breath"

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok, so it does look like it's asking for \(c_4\), but I'm not seeing where you'd put in the 4

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I think I have to come up with c1 first, so I have to have a discrete time dynamical system so that I can plug in c1 and do it 4 times to get to c4. Also I am assuming that c0=1 (initial value)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok, so you're supposed to do iterations. that makes sense

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Is the 1 supposed to be in the subscript?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Like this? \[C_1=(10.3)(0.2)+(0.3)(0.2)\] And then use this to find \(C_2\)?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes, iteration! I think you are on to something... so for C4  let me see what I get...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so wait shouldn't the 0.2 be 0.1, since the concentration is now 10%?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I meant the 0.3 sorry not the 0.2

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yes it's 0.1 \(C_{t+1}=(1q)C_t+q \gamma\) \(C_t\) is the only thing that changes, so the equation is basically \(C_{t+1}=(1  0.1)C_t+(0.1)(0.2)\) \(C_{t+1}=0.9C_t+0.02\) Then iterate \(C_{1}=0.9(0.1)+0.02=0.11\) \(C_{2}=0.9(0.11)+0.02=0.119\) \(C_{3}=0.9(0.119)+0.02=0.1271\) \(C_{4}=0.9(0.1271)+0.02=0.13439\) So the concentration after 4 breaths is 13.4%. That's what I'm thinking anyway
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