Question

You will write a short (less than two pages double-spaced) paper. The paper may include diagrams, graphs, or screenshots.

Your boss has given you the following data table. The table shows the temperatures y (in degrees Farenheit) in a city over a 24-hour period. Let x represent the time of day, where ? = 0 corresponds to 6 a.m.

time, x Temperature y

0 34

2 50

4 60

6 64

8 63

10 59

12 53

14 46

16 40

18 36

20 34

22 37

24 45

These data can be modeled approximately by the polynomial function,

?=0.026?3 −1.03?2 +10.2?+34, 0≤?≤24

(a) Use a graphing utility (calculator or some on-line app) to create a scatter plot of the data. Then graph the polynomial in the same viewing window.
(b) What is your informed opinion about how well the function fits the data?
(c) Use the graph to approximate the times when the temperature was increasing and decreasing. (d) Use the graph to approximate the maximum and minimum temperatures during this 24-hour period.

(e) Write a memo to your boss explaining your steps and your answers in (a) through (d). Include any graphs necessary to explain yourself.

Answer 1