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

3000

4000

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 Schoolsdiane.leighty@powhatan.k12.va.us

Powerpoint will be posted to website:www.powhatan.k12.va.us/teachers/dleighty/Dleighty.htm