Saturday, October 2, 2010

A Deluge

This week saw massive rains in Vermont and elsewhere up and down the East Coast . The intensity of the rains and subsequent flooding are described in this article taken from the Brattleboro Reformer:

Flooding closes Vt. roads, state offices as storm slams East coast

Here in Putney, we were watching the Connecticut River pretty closely as our school keeps a number of rowing shells in a boathouse on the riverside and if the river floods over the banks, the results would be disastrous.

In looking into the situation, our crew coach used this graph, which she sent along to all the faculty to see if we might use it in our classes.

Since I was right at the end of a unit on functions, it provided an exceptional context to highlight and really use the concepts and vocabulary we had just encountered:

1. Find the average rate of change of the water level (stage) from 10AM Friday to 10AM Saturday.

2. During what 6 hour time period was the rate of change the largest, and what was that rate of change?

If the stage continued to decrease at the steady rate predicted by the green portion of the graph, when do you predict the level will return to the minimum level shown on September 29th?

Notice that the independent dependent variable (the so-called “y-axis”) is scaled in two different ways: the left hand scale gives the rivers stage in feet as a function of time and the right hand scale gives the river’s flow in kcfs as a function of time. Find the average rate of change of flow during the 6 hour time period you picked in question #2. Please be sure to give your answer with a correct unit

Finally, make a table in which you use stage as the independent variable and flow as the dependent variable. Enter 10 pairs of values in the table, then graph this data with Geogebra.

In the INPUT BAR, enter the command FITPOLY[A,B,C,D,…,I,J,2] where A through J are the names Geogebra assigned to your points. This instructs Geogebra to make a 2nd degree polynomial (a quadratic function) that fits the data you provided.

What happens to the rate of change of flow to stage as the stage gets greater?

Think about the physical mechanics of a river and give an explanation as to why this relationship should NOT be linear.

Now, I used a quadratic regression, just because I quickly saw that it fit pretty well. I have no idea right now if it's the best model, but it was a nice way to introduce the students to that command in Geogebra.

The document I gave the students to work from is available here.