Warming, Cooling,
and Urban Ozone Pollution
Part 2: The Cooling
Curve
The data for the cooling
curve are entered in your worksheet. Because we are not considering the
warning curve at this point, the time scale has been reset to start when
the cooling starts.
- Plot the data.
- Recall that the ambient
temperature for the data is 72.3 degrees F. Subtract this number from each
data point and plot again on an appropriate vertical scale.
- Now plot the scaled data
on a semilog scale. Does this confirm -- at least approximately -- that
the scaled data decay exponentially?
- Find the decay constant
k.
- You now have all the information
you need to write down a formula for an approximate model function for
this data. On your plot of the original data, superimpose the graph of
the model function to confirm that you have the right numbers.
- Next we check the fit of
the Newton model a second way. Use the commands in your worksheet to compute
symmetric difference quotients that approximate the derivative of temperature
with respect to time. Then plot these approximate values of the derivative
against temperatures. Is the derivative a linear function of temperature?
(At best we expect only a rough fit, because we can't compute our difference
quotients on very small intervals.)
Send comments to the
authors <modules at math.duke.edu>
Last modified: October 21,
1997
