Exponents in the Real World

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2. Computer Games use "Game Physics Engines" which
are low level programs inside the game to calculate the
movement, interactions, and the geometry involved with
the game.
These programs use lots of Algebra formulas in their
Algorithms, and many of these formulas involve multiplying
powers terms containing exponents.
If the mathematics isn't correct in
the game engine, then the game
is not going to play at all like we
would expect it to.
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3. If One Person , tells another 10 people, and then each of these
10 people tell another 10 people, and so on, we get rapid spreading
of a message, video, photo, news item, or product across the Internet.
Level 0 1 2 3 4 etc
Spread 1 + 10 + 100 + 1000 + 10 000
Powers 100 101 102 103 104
Spread = 10
Level
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4. Money Invested that earns interest on the interest, follows an
Exponential rate of growth to produce large amounts of money.
Eg. Retirement Funds, Long Term Investments, and Property.
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5. If we have One Person and they have 4 children, and then
each of these children have 4 children, and so on, we get the
following Exponential Population Growth.
Generation 0 1 2 3 4
Children 1 4 16 64 216
Powers Values (20)2
(21)2
(22)2
(23)2
(24)2
Rule: (2Generation)2
Children 1 4 16 64 216
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6. The World’s Population is growing at an Exponential Rate.
Most of the growth is in developing countries where many people
are having many children. How will they all be accommodated?
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7. With World’s rapidly growing population in recent years, Fossil
Fuel use for Industry and Transportation has gone “through the
roof”. (Eg. A Huge Exponential Increase in fuel consumption).
Image Source: http://oilprice.com

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At first only a few people had smart phones, then within only a
few years, it seems that everybody has an iPhone or similar.
Eg. The Growth in Smart Phone usage has been Exponential.

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Credit Card Debt was growing exponentially, until the Global
Financial Crisis dramatically slowed down consumer spending.

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Once Bacteria and Mould start growing on food that is not
refrigerated, it reaches harmful levels very quickly.

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Viruses such as Flus, and HIV AIDS can spread at Exponential
Rates causing Epidemics affecting millions of people.

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In an uncontrolled Nuclear Explosion, Energy increases at
an Exponential Rate as per Einstein’s Equation: E = mc2
.

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Straight Line graphs represent steady increases, but Exponential
Curve Graphs show growth happening at a faster and faster rate.

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There is also Exponential Decrease, or “Decay”, which occurs when
we raise Fractions to Powers. In this type of decrease, things drop
down reasonably fast at first, but then get slower and slower.

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The volume of sound decreases in a 1 / Distance x Distance, or
1 / d2
, or d-2
relationship. Move 4 times further away, and the
sound level is only 1/16th of what it was. Sound dies off “quickly”
as we move away from a loud party or car, but takes a while to
drop down to complete silence.

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The light intensity from a Projector, or detected by a Camera,
also follows the Inverse Square of a 1 / d2
type relationship.

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If a knock-out Tennis Competition starts with 64 players, how
many rounds will it take to reach the Grand Final ?
Round 0 1 2 3 4 5
Players 64 32 16 8 4 2
Fraction 64/(20) 64/(21) 64/(22) 64/(23) 64/(24) 64/(25)

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High Level Radioactive Waste (HLW), from Nuclear Power Plants
takes thousands of years to reduce down to a safe level.

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The “Richter Scale” quantifies the amount of seismic energy, (as
the Indexes of Powers of 10), that is released by an earthquake.

22. Image Source: http://online.wsj.com
The pH scale also uses Power of 10 Exponents, for how Acidic or
Alkaline a substance is. Public Swimming Pools maintain a pH
between 7.0 and 7.4 to provide the best possible comfort levels
for the public, as well to ensure effective chlorine action.

23. Image Source: http://nerdsoftheroundtable.wordpress.com
Powers of 10 Exponents, (called Scientific Notation), are used to
specify very large amounts, such as the distance between stars
and Planets. Earth to Moon Distance is about 4 x 105
km.

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Negative Powers of 10 Exponents, (called Scientific Notation), are
used to specify very small decimal amounts, such as the distance
between Silicon atoms in a Silicon Crystal which is 2.35 x 10-10
m.

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