Aboard an orbital research station, Nova and Luna prepared to transmit a large data file as a satellite passed overhead. A graph showed signal strength, S, as a function of time, t, during a 12-minute communication window. At t = 0, the signal strength was 20 units. It increased steadily until reaching a maximum of 92 units at t = 7 minutes, then decreased to 35 units by t = 12. Luna identified the function as increasing from 0 to 7 minutes and decreasing from 7 to 12 minutes. Nova compared several points on the graph: the signal measured 68 units at 4 minutes and 74 units at 10 minutes, but neither matched the maximum. They concluded that transmitting near t = 7 minutes would provide the strongest connection. Nova started the transfer at the peak, and the complete data file reached the satellite successfully.

Challenges

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Challenge 1 of 5

Challenges

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Challenge 1 of 4
Hint
Compare the signal strength before and after its maximum at 7 minutes.
Which statement correctly describes how the satellite signal strength changes during the 12-minute communication window?
It decreases from 0 to 7 minutes and increases from 7 to 12 minutes.It increases throughout the entire 12-minute window.It increases from 0 to 7 minutes and decreases from 7 to 12 minutes.It remains constant from 0 to 7 minutes and then decreases.
Correct! The signal increases until t = 7 minutes and then decreases.
Not quite. Use the maximum at t = 7 minutes to separate the increasing and decreasing parts of the function.
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Hint
First find the average of 68 and 74, then compare it with 92.
The signal strength is 68 units at 4 minutes, 92 units at 7 minutes, and 74 units at 10 minutes. How many units greater is the maximum signal strength than the average of the signal strengths at 4 and 10 minutes?
Correct! The average is 71 units, and the maximum is 21 units greater.
Try again. Add 68 and 74, divide by 2, and then subtract the result from 92.
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Hint
Compare the signal values at the three possible starting times and identify the greatest value.
Nova can begin the data transfer at 4, 7, or 10 minutes. If the goal is to begin when the signal is strongest, which choice is best supported by the function values in the story?
Begin at 4 minutes because the signal is still increasing and measures 68 units.Begin at 7 minutes because the signal reaches its maximum value of 92 units.Begin at 10 minutes because 10 is the greatest time value and the signal measures 74 units.Any of the three times is equally good because they are all in the same communication window.
Correct! The signal is strongest at 7 minutes, when it reaches 92 units.
Not quite. The best starting time is the one associated with the greatest signal strength.
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Uydu Sinyali Zaman Aralığı
TR
ARC_G10_PA_02_STORY_01
Uydu Sinyali Zaman Aralığı
The Satellite Signal Window
EN
ARC_G10_PA_02_STORY_01
The Satellite Signal Window