# Math

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111. Cold Water Survival When a person falls through the ice on a lake, the cold water removes body heat 25 times faster than air at the same temperature. To survive, a person has between 30 and 90 seconds to get out of the water. How long could a person remain in air at the same temperature?

81. Aging More Slowly Albert Einstein in his theory of relativity showed that if a person travels at nearly the speed of light, then time slows down significantly. Suppose that there are twins; one remains on Earth and the other leaves in a very fast spaceship having velocity v. If the twin on Earth ages To years, then according to Einstein the twin in the spaceship ages years, where
T(v) = To sqrt(1-(v/c)^2))
In this formula c represents the speed of light, which is 186,000 miles per second.

21. Heart Rate of an Athlete The following table lists the heart rate or pulse of an athlete running a 400-
meter race. The race lasts 50 seconds.

Time (seconds) 0 20 30 50
Heart Rate (bpm) 100 134 150 180

(a)Does model the data in the table exactly? Explain.

Pt = - (1/300)t^2 +(53/30)t + 100

(b) Does P*(60) have significance in this situation? What should be the domain of P?

69. Motor Vehicle Fatalities The number of motor vehicle deaths increased by 13.75 times from 1912 to 2003. There were 39,525 more deaths in 2003 than in 1912. Find the number of motor vehicle deaths in each of the two years. Note that the number of motor vehicles on the road increased from 1 million to 230 million between 1912 and 2003. (Source: Department of Health and Human Services.)