Plotting Temperature and Altitude

Objective:

--Students will experience a real-life application of linear graphing and gain experience moving between and among the different representations of functions.

--Students will also be given practice with computing slope and describing what the slope represents.

Background:

--In September 1995, Pathfinder reached an altitude of 50,500 feet. In April 1997, Pathfinder was shipped to Kauai, Hawaii. Kauai was chosen as a location for testing the solar-powered Pathfinder due to high levels of sunlight. There it flew seven high-altitude flights including a world record altitude flight of 71,530 feet. As an aircraft flies higher and higher, the temperature in the atmosphere decreases at a nearly constant rate. For every 1,000 feet gained in altitude, up to 36,000 feet, the temperature decreases by 5.4 degrees Fahrenheit (This is called the value of the lapse rate).

Activity:

1. Provide students with data collected in August of 1997. This data shows the relation between the altitude and the temperature.

2. Students will observe and discuss any patterns in the data. Students will make a raw sketch of what they think the graph of altitude (x-axis) versus temperature (y-axis) might look like.

3. Using the data above, students will create a graph and compare it with the sketch above.

4. Ask the students to convert the temperature readings from degrees Celsius into degrees Fahrenheit. F=(9/5)C + 32.

5. Ask students to predict and create a graph. Students should notice that regardless of the unit of measurement the temperature still decreases as altitude increases.

6. The student will choose any two data points and compute the slope.

slope= m=(y_{2} -y_{1}) / (x_{2} -x_{1})

Shown below is the calculation of slope for the points (25, 3.02) and (30, -17.68).

slope = m = (Y2 - Y1) / (X2 - X1)

slope = m = (-17.68 - 3.02) / (30 - 25)

slope = m = -20.7 / 5

slope = m = -4.14 7. Ask the student what the slope represents. Also keep in mind that slope refers to a rate of change.

Thus, the slope of the line between these two points is -4.14. In other words, the rate at which the temperature is changing with altitude is -4.14 degrees Fahrenheit. The slope has a negative value because the temperature is decreasing.

8. Compare the computed values for the lapse rate to the actual value. Are
they the same? Different? Why might the actual lapse rate not exactly match the
computed values. Discuss.