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Full

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by

Blake Yarbrough

on 19 November 2009

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Transcript of Full

Small World Here Is our old 'best' curve... This guy gives us a 2009 population
with four points precision (6.7769 bil) The formula for this curve is
4.7E8(e^(.0147270714*(X-177.8))) Here Is the sexy curve... This guy is our most accurate yet
with five points precision (6.77698 bil) The golden formula here (after much tweaking)
4.7E8 * e ^ (0.0147570714 * (X - 177.8322)
You may be wondering what this is all about, so here is a convenient preface just for you! We were challenged to create a pretty
little model. This model is to be in
the form of a formula for a curve.
The curve is to model the human
population growth based on a
number of arbitrary points (and
a few that are more accurate
or maybe you prefer precise)
either way that's it. For the sake of understanding
we will walk you through the
means of manipulating a formula
for growth that is in the form of
y = k * e ^ (c * x) for this explanation we will use the example fomula y = 5 * e ^ (4 * x) Oh yeah, e is a constant
with a rough value of
2.71828183 according to
our buddies at Google Curve Fitting: An Overview So here is the graph... The formula y = 5 * e ^ (1 * x)
will act as our base function here As you manipulate the k
value (in this case five) you
alter the y intercept of the
graph and the steepness
of the graph. For the sake of understanding
we will walk you through the
means by which formulas for a
curve are manipulated when in
the form
y = k * e ^ (c * x) Oh yeah, e is a constant
representing a value of
2.71828183, according
to our buddies at Google here we have curves for
k = 10, k = 5, and k = 1 As we alter the value of c
we can change the severity
of the curve while maintaining
the y intercept (our number at
which x = 0) Here we have a graph
where c= 1, c = 2, and
c = 0.5 Another key concept is the
manipulation of x by adding and subtracting. This translates the graph
along the x-axis and affects the
severity of the curve. Here is the graph where
x is unaffected, increased
by two and decreased by two. the population values we were
given are as follows
year population
1650 470,000,000
1750 694,000,000
1850 1,091,000,000
1900 1,570,000,000
1950 2,510,000,000
1960 3,030,000,000
1970 3,680,000,000
1980 4,480,000,000
1985 4,487,000,000
1990 5,290,000,000
1995 5,730,000,000 Look at those points ahhh...nice Now that we have our points
it is time to fit a curve to them! The formula for the beautiful curve
offers us some fearsome predictions The population should double around
the year 2056 (coincidentally the year
in which Ghost in the Shell is set) and it will triple in 2083 The real troubling revelation
requires a bit of information
to understand the gravity of. The surface area of all the
land on our planet is
~ 1.6 * 10 ^ 15 square feet By our models' predictions the human population
of the Earth will be 1.6 * 10 ^ 15 at the year 2847 When you consider that long before
there is only one square foot of land
per human being, we will reach a
critical issue of living space. Consider
for a moment; trees, mountains, poles
other creatures, etc. All things that do
not permit us to reach 1.6 * 10 ^ 15 After considering such,
the clear revelation is that
we are an awful lot closer
to a fearsome number that
will result in war, pestilence,
or genocide. Optimism: it's a virtue Thank You for
allowing us to
administer your
daily dose of
depression
Full transcript