At 6:00 am, here's what we know about two airplanes: Airplane #1 has an elevation of 31690 ft and is descending at the rate of 100 ft/min. Airplane #2 has an elevation of 14900 ft and is descending at the rate of 500 ft/min. At 6:25 am, Airplane #2 quickly levels off its flight and flies horizontally. At 6:40 am, this plane then begins to climb at 350 ft/min. (1) Let t represent the time in minutes since 6:00 am, and let E represent the elevation in feet. Write an equation for the elevation of each plane in terms of t. Note that the equation for plane #2 will have 3 separate pieces. plane #1: E(t) = plane #2 (descent): E(t) plane #2 (steady elevation): E(t) plane #2 (ascent): E(t) (2) At what time will the two airplanes have the same elevation? minutes after 6:00 am (3) What is the elevation at that time? E feet

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Chapter3: Polynomial Functions
Section3.5: Mathematical Modeling And Variation
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At 6:00 am, here's what we know about two airplanes: Airplane #1 has an elevation of 31690 ft and is
descending at the rate of 100 ft/min. Airplane #2 has an elevation of 14900 ft and is descending at the rate
of 500 ft/min.
At 6:25 am, Airplane #2 quickly levels off its flight and flies horizontally. At 6:40 am, this plane then begins
to climb at 350 ft/min.
(1) Let t represent the time in minutes since 6:00 am, and let E represent the elevation in feet. Write an
equation for the elevation of each plane in terms of t. Note that the equation for plane #2 will have 3
separate pieces.
plane #1: E(t) =
plane #2 (descent): E(t)
plane #2 (steady elevation): E(t)
plane #2 (ascent): E(t)
(2) At what time will the two airplanes have the same elevation?
minutes after 6:00 am
(3) What is the elevation at that time?
E
feet
Transcribed Image Text:At 6:00 am, here's what we know about two airplanes: Airplane #1 has an elevation of 31690 ft and is descending at the rate of 100 ft/min. Airplane #2 has an elevation of 14900 ft and is descending at the rate of 500 ft/min. At 6:25 am, Airplane #2 quickly levels off its flight and flies horizontally. At 6:40 am, this plane then begins to climb at 350 ft/min. (1) Let t represent the time in minutes since 6:00 am, and let E represent the elevation in feet. Write an equation for the elevation of each plane in terms of t. Note that the equation for plane #2 will have 3 separate pieces. plane #1: E(t) = plane #2 (descent): E(t) plane #2 (steady elevation): E(t) plane #2 (ascent): E(t) (2) At what time will the two airplanes have the same elevation? minutes after 6:00 am (3) What is the elevation at that time? E feet
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