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Exponential model The following table shows the time of useful consciousness at various altitudes in the situation where a pressurized airplane suddenly loses pressure. The change in pressure drastically reduces available oxygen, and hypoxia sets in. The upper value of each time interval is roughly modeled by T = 10 · 2−0.274a, where T measures time in minutes and a is the altitude over 22,000 in thousands of feet (a = 0 corresponds to 22,000 ft).
Altitude (in ft) | Time of Useful Consciousness |
22,000 | 5 to 10 min |
25,000 | 3 to 5 min |
28,000 | 2.5 to 3 min |
30,000 | 1 to 2 min |
35,000 | 30 to 60 s |
40,000 | 15 to 20 s |
45,000 | 9 to 15 s |
- a. A Learjet flying at 38,000 ft (a = 16) suddenly loses pressure when the seal on a window fails. According to this model, how long do the pilot and passengers have to deploy oxygen masks before they become incapacitated?
- b. What is the average rate of change of T with respect to a over the interval from 24,000 to 30,000 ft (include units)?
- c. Find the instantaneous rate of change dT/da, compute it at 30,000 ft. and interpret its meaning.
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