Functions Defined by Data MATH IN FLIGHT. First Class Postage Rates YearPostage (cents) YearPostage...
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Transcript of Functions Defined by Data MATH IN FLIGHT. First Class Postage Rates YearPostage (cents) YearPostage...
Functions Defined by Data
MATH IN FLIGHT
First Class Postage Rates Year Postage
(cents)Year Postage
(cents)
1885 2 1976 13
1918 3 1978 15
1919 2 1981 18
1932 3 1982 20
1958 4 1985 22
1963 5 1988 25
1968 6 1991 29
1971 8 1995 32
1974 10 1999 33
(Source of data: Associated Press, 7/2/2000.)
Postage Stamp
0
5
10
15
20
25
30
35
1860 1880 1900 1920 1940 1960 1980 2000 2020
Year
Cost
of O
ne F
irst-C
lass
Sta
mp
Piecewise Solution1885 To 1958
y = 0.0274x - 49.857
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
1880 1900 1920 1940 1960 1980
Year
Cost
of S
tam
p (c
ents
)
1963 To 1999
y = 0.8984x - 1761.4
0
5
10
15
20
25
30
35
40
1960 1965 1970 1975 1980 1985 1990 1995 2000 2005
Year
Cost
of S
tam
p
• The year is 2006. The current price of a first-class stamp is $0.39. Does this fit the trendline?
• From the data, what do you predict the price of a stamp will be in 2010?
Path of Object
0
1000
2000
3000
4000
5000
6000
7000
0 20 40 60 80 100 120 140
Time (minutes)
Dist
ance
(fee
t)
What is this?
Mystery Data
• Dist vs. Time data• How fast is the object moving?• Is the speed changing?• Connections to distance vs. time graph?• (For fun): what is this object?
Path of Object
0
1000
2000
3000
4000
5000
6000
7000
0 20 40 60 80 100 120 140
Time (minutes)
Dist
ance
(fee
t)
Calculator Lists: TIMEA and TDIST
Time(s) Total Dist(ft) Time(s) Total Dist(ft) Time(s) Total Dist(ft)
0 0 12 1564 24 2834
1 137 13 1682 25 2926
2 275 14 1800 26 3017
3 412 15 1919 27 3105
4 545 16 2029 28 3193
5 679 17 2136 29 3277
6 809 18 2243 30 3361
7 942 19 2346 31 3441
8 1068 20 2453 32 3521
9 1198 21 2552 33 3601
10 1324 22 2643 34 3677
11 1442 23 2743 35 3754
Path of Object
0
1000
2000
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5000
6000
7000
0 20 40 60 80 100 120 140
Time (minutes)
Dist
ance
(fee
t)
Change in Distance wrt Time
0
20
40
60
80
100
120
140
160
0 20 40 60 80 100 120 140
Time (sec)
Chan
ge in
Dis
tanc
e (ft
)
Time (s) Distance
(ft) Time (s) Distance
(ft) Time (s) Distance
(ft)1 137 13 118 25 92
2 138 14 118 26 91
3 137 15 119 27 88
4 133 16 110 28 88
5 134 17 107 29 84
6 130 18 107 30 84
7 133 19 103 31 80
8 126 20 107 32 80
9 130 21 99 33 80
10 126 22 91 34 76
11 118 23 100 35 77
12 122 24 91 36 72
Calculator Lists: TIMEB and DDIST
http://flightaware.com/live/
• Flight Aware Live Tracker Web Page• Select a plane type – Boeing 767• Select a flight – Delta Flight -
– Cincinnati to Atlanta• Select STATUS to see details of flight
32.5
33
33.5
34
34.5
35
35.5
-85 -84.5 -84 -83.5 -83 -82.5 -82 -81.5 -81 -80.5
FLIGHT PATH
0
50
100
150
200
250
300
350
400
450
0 10 20 30 40 50 60 70
Distance Traveled (miles) vs. Time (min.)
TRIPy = 6.8707x - 0.2906
-50
0
50
100
150
200
250
300
350
400
0 10 20 30 40 50 60
Time (min)
Tota
l Dis
tanc
e
Trip
Linear (Trip)
Altitude (ft) vs. Time (min)
0
5000
10000
15000
20000
25000
0 10 20 30 40 50 60
Time (min)
Altit
ude
(ft)
Piecewise FunctionAltitude
0
5000
10000
15000
20000
25000
0 2 4 6 8 10 12
Time (min)
Altit
ude
(ft)
Altitude
y = 2172.4x + 923.53
0
5000
10000
15000
20000
25000
0 2 4 6 8 10 12
Time (min)
Altit
ude
(ft)
Altitude
Linear (Altitude)
For 0 < t < 10 sec.
Altitude (ft) vs. Time (min)
0
5000
10000
15000
20000
25000
0 10 20 30 40 50 60
Time (min)
Alti
tude
(ft)
Middle Piece10 < t < 42
0
5000
10000
15000
20000
25000
0 5 10 15 20 25 30 35 40 45
Time (min.)
Altit
ude
(ft)
2nd Piece
y = 22000
0
5000
10000
15000
20000
25000
0 5 10 15 20 25 30 35 40 45
Time (min)
Altit
ude
(ft)
10 < t < 42
Finish with Model of Descent
0
5000
10000
15000
20000
25000
0 10 20 30 40 50 60
Time (min)
Alti
tude
(ft)
Atlanta to DullesFlight From Atlanta, GA to Dulles, Washington DC
0
100
200
300
400
500
600
0 10 20 30 40 50 60 70 80 90 100
Time (minutes)
Gro
und
Spee
d (m
ph)
Atlanta to Dulles
0
5000
10000
15000
20000
25000
30000
35000
40000
0 10 20 30 40 50 60 70 80 90 100
Time (minutes)
Altit
ude
(ft)
Collect Live Data
• Students can collect live data• Model the data they collect with
mathematical equations.• Linear to Quadratic to Other models• Rate of Change – Average to
Instantaneous for Precalculus to Calculus
Thank YouDiane LeightyMathematics CoordinatorPowhatan County Public [email protected]
Powerpoint will be posted to website:www.powhatan.k12.va.us/teachers/dleighty/Dleighty.htm