Math Connections

Title: How Long Do I Have To Hold My Breath?

Background: Asthma is an increasingly common breathing disorder among students. Some people minimize its risks but not being able to inhale enough air is a panicky situation. And, maybe each of us has heard of someone dying from complications relating to asthma.

             Although air pollution has not been positively identified as the cause of asthma, it is suspected of being a “trigger” setting off attacks in people who already have the condition. If asthmatics know bad air is on the way, they are able to plan their activities to minimize exposure to it and reduce the chance of an asthma attack. A “bad air” warning system might provide data about the speed and direction of the approaching air mass.

Process: Answer the following questions.

Questions.

Data

time (days): 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

distance (km): 16 30 45 67 79 101 110 126 144 162 176 194 205 221 238 257

1. Plot the graph. (Axis values? Axis scales? Axis labels and units?)

2. a) Find the slope of the graph’s best fit line. (Make a smooth line, not point-to-pont.)

    b) What does the slope tell us about the motion of the air mass? (Slope units?)

3. Find the equation for the plot.

4. How could this data about the motion of the air mass have been collected?

5. Do the following data fit the existing pattern?

    4.5 days, 80 km 6.2 days, 105 km 10.7 days, 170 km 13.2 days, 250 km

    Note: test the new data visually and mathematically.

6. a) Use the graph to predict when the air mass will reach us if we are located 400 km from its source.

    b) Use the plot equation to predict how far the air might travel in 20 days.

7. What are some types (not names) of industries suspected of releasing of bad air?