Linear and exponential growth
Aug. 8, 2010 (the 2010 Avinor link has since been slightly modified,
but reconstruction of data should be possible):"Record in flight
traffic from Oslo Airport Gardermoen in July 2010”
news headlines said yesterday,also the Norwegian governmental flight
inspection two months ago recommended doubling of the capacity of this
12 year old airport by expanding terminals and facilities at all.
Linear growth can be described by the equation f(x) = ax + b or
visualised either in a coordinate system or by setting up a
table.Official data over international aircraft movements (takeoffs and
landings) from Oslo Airport are available at Avinor. Movements
in thousands for the period 2003-2008 are tabularised here:
| 2003 | 79.662 |
| 2004 | 90.219 |
| 2005 | 95.266 |
| 2006 | 106.025 |
| 2007 | 111.504 |
| 2008 | 116.227 |
On the B&W calculator screen shots we see table + graph of the data,also the calculated values of the constants a and b (a is the slope of the graph with x axis in years and y axis in thousands of aircraft movements.b is the graphs y intercept).
Exponential growth is illustrated by the righhtmost graph showing
increase in atmospheric CO2 content from 1700 to 1995 with value in
1700 0.028%, 1995 0.035% and latest (not shown) june 2010 0.0392 %.
Exponential growth can algebraically be expressed by the formula f(x) =
ba^x (where b correspond to the y intercept of the curve).a will be the
base of the function.
When a mathematical model describing correlations is found (here
aircraft movements and atmospheric CO2 content as functions of time)
predictions and analysis can be done.The June 2010 figure of
CO2 is an example of a precise prediction as the value fits
well on the extrapolated (exponential) 1700-1995 growth curve.
Climate is dependent on many factors and meteorologists have found a
rough linear corellation between atmospherical CO2 content and
temperature - when CO2 rise, so do temperature.Early this millennium Al Gore campaigned on climate change and the
movie “An inconvenient truth” was released January 2006 - without much
success as things seem to be rather “business as usual”.Politicians and other delegates at the climate conference in Copenhagen
must have been aware of facts and elementary math, also because many of
those elected now have economical background and will know about growth
(the equation f(x) = ba^x even describe growth of a plain bank account).
CO2 emitted at high altitude probably exist for longer than the
average 120 years.Rise in flight traffic should be reversed if
representatives wants lower levels of climate gases.I believe most
international travel is for leisure, even much business and official
travel are of no significant importance.It is against common sense
when seasonal workers from Indochina are flown to and from Scandinavia
to pick berries when domestic unemployment exist.
People in the future will appreciate fractions of degrees in
temperature rise inhibited.The climate issue should not be difficult
for those elected to deal with - share a significant part of our wealth with
those exploited and set the standard of living back to what it was in
the 1980’s - it was not that bad at all.It is all a question of
values, or lack of.