The table shows the temperatures y (in degrees Fahrenheit) in a city over a 24 -hour period. Let x represent the time of day, where x = 0 corresponds to 6 a.m. These data can be approximated by the model y = 0.026 x 3 − 1.03 x 2 + 10.2 x + 34 , 0 ≤ x ≤ 24. (a) Use a graphing utility to create a scatter plot of the data. Then graph the model in the same viewing window. (b) How well does the model fit 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) Could this model predict the temperatures in the city during the next 24-hour period? Why or why not?
The table shows the temperatures y (in degrees Fahrenheit) in a city over a 24 -hour period. Let x represent the time of day, where x = 0 corresponds to 6 a.m. These data can be approximated by the model y = 0.026 x 3 − 1.03 x 2 + 10.2 x + 34 , 0 ≤ x ≤ 24. (a) Use a graphing utility to create a scatter plot of the data. Then graph the model in the same viewing window. (b) How well does the model fit 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) Could this model predict the temperatures in the city during the next 24-hour period? Why or why not?
Solution Summary: The author explains how to draw the scatter plot and graph of the model in the same viewing window by using the graphing utility.
The table shows the temperatures
y
(in degrees Fahrenheit) in a city over a
24
-hour
period. Let
x
represent the time of day, where
x
=
0
corresponds to 6 a.m.
These data can be approximated by the model
y
=
0.026
x
3
−
1.03
x
2
+
10.2
x
+
34
,
0
≤
x
≤
24.
(a) Use a graphing utility to create a scatter plot of the data. Then graph the model in the same viewing window.
(b) How well does the model fit 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) Could this model predict the temperatures in the city during the next 24-hour period? Why or why not?
Definition Definition Representation of the direction and degree of correlation in graphical form. The grouping of points that are plotted makes it a scatter diagram. A line can be drawn showing the relationship based on the direction of points and their distance from each other.
Manuel is investigating how long his phone's battery lasts (in hours) for various brightness levels (on
a scale of 0-100). His data is displayed in the table and graph below.
Brightness Level (x)
30
49
65
67
69
80
85
85
Hours (y)
6.6
4.6
4.1
4.3
3.5
2.8
3.1
10+
7
2
10
20
30
40
60
70
80
100
Brightness Level
a) Find the equation for the line of best fit. Keep at least 4 decimals for each parameter in the
equation.
SANOH
Are cigarettes bad for people? Cigarette smoking involves tar, carbon monoxide, and nicotine (measured in milligrams). The first two are definitely not good for a person's health, and the last ingredient can cause addiction.
Use the data in the table above to make a stem-and-leaf display for milligrams of nicotine per cigarette smoked. In this case, truncate the measurements at the tenths position and use two lines per stem. (Enter NONE in any unused answer blanks.)
Luis is investigating how long his phone's battery lasts (in hours) for various brightness levels (on a
scale of 0-100). His data is displayed in the table and graph below.
Brightness Level (x)
31
33
43
76
81
85
91
95
Hours (y)
4.6
3.2
5.6
2.9
3.1
3.1
2
5-
10
20
30
40
50
60
70
80
90
100
11
Brightness Level
a) Find the equation for the line of best fit. Keep at least 4 decimals for each parameter in the
equation.
b) Interpret the slope in context.
O Luis should expect -0.0331 hours per brightness level.
O Luis should expect -0.0331 brightness level per hour.
c) What does the equation predict for the number of hours the phone will last at a brightness level
of 43?
hours
Hours
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