1.3 Exponential Growth

__1.3____ ____Exponential____ ____Growth__

*Figure** **1.3.1** **Mathematical** **Representation** **of** **Exponential** **Growth:[**see reference **3]*

Figure
1.3.1 sourced from Wikipedia (Author: McSush) under a the Creative Commons CC0
1.0 Universal Public Domain Dedication License

http://en.wikipedia.org/wiki/File:Exponential.svg

The
above
graph
shows
three
different
functions
increasing
over
time.
The
y
axis
is
the
amount
of
something;
the
x
axis
is
increasing
time. The red graph increases
proportionally,
the
blue
increases
cubically,
and
the
green
graph
increases
exponentially. In this example
the
exponential
graph
doubles
over
a
set
period
of
time
but
it
could
triple,
quadruple
or
increase
by
any
factor
of
x
over
time.

The
green
graph
is
the
important
one
as
it
is
this
model
that
many
world
systems
such
as
population
growth
and
resource
consumptions
follow. The shape of
that
graph
and
the
concepts
it
introduces
are
essential
to
understanding
the
trajectory
of
patterns
in
society.

*Example:**
**A**
**bacteria**
**is**
**introduced**
**to**
**a**
**lake**
**of**
**a**
**finite**
**size.** **The** **bacteria**
**cover**
**a**
**set**
**area**
**of**
**the**
**surface**
**of**
**the**
**lake,**
**and**
**this**
**area**
**doubles**
**in**
**size**
**every**
**hour.** **After** **1**
**hour**
**the**
**bacteria**
**covers**
**1%**
**of**
**the**
**lake.** **How** **many**
**hours**
**will**
**it**
**take**
**to**
**cover**
**the**
**whole**
**lake?*

*It** **takes**
**6**
**hours**
**for**
**the**
**bacteria**
**to**
**cover**
**just**
**under**
**one**
**third**
**of**
**the**
**lake**
**(32%),**
**but**
**in**
**the**
**next**
**hour**
**and**
**a**
**half,**
**it**
**covers**
**the**
**whole**
**of**
**the**
**lake.**
**This**
**example**
**is**
**intended**
**to**
**demonstrate**
**the**
**nature**
**of**
**exponential**
**growth**
– **amounts**
**become**
**very**
**large**
**very**
**quickly.*

It could be
considered
that
we
are
now
in
that
final
hour,
where
the
amount
of
water
left
on
the
lake
is
our
remaining
resources. If it is known that
the
world
is
strained
with
our
presence
currently,
those
strains
will
double
in
a
short
period
of
time,
and
double
again
after
that
unless
radical
changes
are
made.