
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN: 9780079039897
Author: Carter
Publisher: McGraw Hill
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Transcribed Image Text:On Feb. 8, this year, at 6am in the morning all UiB meteorology professors met to discuss a highly unfortunate
and top-urgent crisis: Their most precious instrument, responsible for measuring the air temperature hour-by-
hour, had failed - what if the Bergen public would find out? How would they plan their weekend without
up-to-date air temperature readings? Silent devastation - and maybe a hint of panic, also - hung in the room.
Apprentice Taylor, who - as always - was late to the meeting, sensed that this was his chance to shine! Could
they fake the data? At least for some hours (until the measurements would work again)? He used to spend a
lot of time online and thus knew the value of fake data, especially when it spread fast!
He reminded the crying professors of a prehistoric project with the title "Love your derivatives as you love
yourself!" - back then, they had installed top-modern technology that not only measured the air temperature
itself, but also its 1st, 2nd, 3rd, 4th, and even its 5th derivatives! Nobody had ever used this research, but today
was different. Proudly, Taylor claimed that he could ensure air temperatures would come out "as usual" for at
least several hours!
Under quite some dust, he quickly found the 6am readings on a fragile looking tape:
T\6am
T'
T"
6am
16am
6am
T!!! T!!!!
2.8 19 -100 100/3 640
T!!!!!
6am
6am
-675
On the label of the tape, he could also read: "time unit: 1 day (24h)", "uncertainty: ±10%", and "careful
with those higher orders!"
With all his love for the KISS principle, Taylor decided to first try the lower orders. He quickly constructed
models fa(t) of increasing degree d = {0, 1, 2, . . ., 5} for t≥ 0 (with t = 0 corresponding to Feb. 8, 6am, and
t = 1 corresponding to Feb. 9, 6am) that would give him fake air temperatures for the coming hours. Write
out these model functions for him (up to order 5).
Then, he decided to evaluate these models for t € 24. {0, 3, 6, 9, 12, 15, 18, 21, 24}, corresponding to the
coming 24 hours (in steps of 3h). Make a 6×9 table with the resulting numbers. If you prefer rounded
decimals, round to at least one digit after the comma. Look critically at your table and think: which entries
seem trustworthy, which maybe not so much? Discuss your observations.
Extra point (not required for "ticking" this exercise as solved): How could the uncertainty-info on the tape
label be used to study, until which time on Feb. 8 (or even Feb. 9) the different models are trustworthy?
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