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# Full

description

by

Tweet## Blake Yarbrough

on 19 November 2009#### 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 transcriptwith 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