Unformatted text preview: ains unchanged. Find
the production level x that maximizes the proﬁt made by producing and selling x PortaBoys.
7. We now revisit the data set from Exercise 4b in Section 2.5. In that exercise, you were given
a chart of the number of hours of daylight they get on the 21st of each month in Fairbanks,
Alaska based on the 2009 sunrise and sunset data found on the U.S. Naval Observatory website. We let x = 1 represent January 21, 2009, x = 2 represent February 21, 2009, and so on.
The chart is given again for reference.
Daylight 1 2 3 4 5 6 7 8 9 10 11 12 5.8 9.3 12.4 15.9 19.4 21.8 19.4 15.6 12.4 9.1 5.6 3.3 Find cubic (third degree) and quartic (fourth degree) polynomials which model this data and
comment on the goodness of ﬁt for each. What can we say about using either model to make
predictions about the year 2020? (Hint: Think about the end behavior of polynomials.) Use
the models to see how many hours of daylight they got on your birthday and then check the
website to see how accurate the models are. Knowi...
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