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Flight Functions Defined by Data: Postage Rates, Piecewise Solution, Predictive Trends

Explore piecewise function in flight data with stamp price trends. Predict stamp price in 2010, analyze speed, distance vs time graphs, mystery data, and connections to math models. Live data collection for mathematical modeling. Contact Diane Leighty for resources.

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Flight Functions Defined by Data: Postage Rates, Piecewise Solution, Predictive Trends

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  1. MATH IN FLIGHT Functions Defined by Data

  2. First Class Postage Rates (Source of data: Associated Press, 7/2/2000.)

  3. Piecewise Solution

  4. 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?

  5. What is this?

  6. 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?

  7. Calculator Lists: TIMEA and TDIST

  8. Calculator Lists: TIMEB and DDIST

  9. http://flightaware.com/live/

  10. 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

  11. FLIGHT PATH

  12. Distance Traveled (miles) vs. Time (min.)

  13. Altitude (ft) vs. Time (min)

  14. Piecewise Function

  15. For 0 < t < 10 sec.

  16. Altitude (ft) vs. Time (min)

  17. Middle Piece

  18. 10 < t < 42

  19. Finish with Model of Descent

  20. Atlanta to Dulles

  21. 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

  22. Thank You Diane Leighty Mathematics Coordinator Powhatan County Public Schools diane.leighty@powhatan.k12.va.us Powerpoint will be posted to website: www.powhatan.k12.va.us/teachers/dleighty/Dleighty.htm

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