Why Exponent Powers Are Important

Image Sources: http://4.bp.blogspot.com and http://img.ehowcdn.com

Power of 2 exponents are the basis of all computing which is done in “Binary” or base 2 numbers like these..

Exponents in Computers

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.

Image Source: http://cheezburger.com

Exponents in Computer Games

Image Source: http://www.singularity.com

Exponents and Viral MarketingIf One Person , tells another 10 people, and then each of these10 people tell another 10 people, and so on, we get rapid spreadingof 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 = 10Level

Image Source: http://m5.paperblog.com

Compound InterestMoney Invested that earns interest on the interest, follows anExponential rate of growth to produce large amounts of money. Eg. Retirement Funds, Long Term Investments, and Property.

Image Sources: http://www.marketoracle.co.uk and http://www.moneyguideindia.com

Population IncreaseIf we have One Person and they have 4 children, and then each of these children have 4 children, and so on, we get thefollowing 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

Image Source: http://backtomyroots.wordpress.com

World Population IncreaseThe World’s Population is growing at an Exponential Rate. Most of the growth is in developing countries where many peopleare having many children. How will they all be accommodated?

Image Source: http://2.bp.blogspot.com

World Fuel ConsumptionWith 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

Smart Phone Uptake and Sales

Image Sources: http://seekingalpha.com and http://www.captees.com

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.

Exponential Growth in Debt

Image Sources: http://peakprosperity.com and http://www.thatslife.com.au

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

Bacteria Exponential Growth

Image Sources: http://foodhygieneasia.com and http://farm6.staticflickr.com

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

Spread of Viruses and Disease

Image Source: http://news.bbc.co.uk

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

Exponential Energy Release

Image Source: http://www.zeusbox.com

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

Exponential Increase Graphs

Image Sources: tutorvista.com http://www.rulesoftheroad.ie http://coachquestions.com http://pixabay.com

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

Exponential Decrease or Decay

Image Source: http://letsmakerobots.com

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

Inverse Square Decrease

Image Sources: http://letsmakerobots.com and http://blog.my.88db.com

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.

Inverse Square Decrease

Image Sources: http://letsmakerobots.com and http://italy.techinlifes.com

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

Exponential Decay

Image Source: www.union.ic.ac.uk

If a knock-out Tennis Competition starts with 64 players, howmany 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)

Half Life Exponential Decay

Image Source: http://www.regentsprep.org

Half Life Exponential Decay

Image Source: http://treehugger.com and http://www.science20.com

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

Exponents and Earthquakes

Image Source: http://lh3.googleusercontent.com

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

Exponents and pH Scale

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.

Exponents and Large Numbers

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 starsand Planets. Earth to Moon Distance is about 4 x 105 km.

Exponents and Small Values

Image Source: http://www.soest.hawaii.edu

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.

Exponents Music VideoThe following music video has had over 850,000 views on YouTube and is quite an amazing Production!http://www.youtube.com/watch?v=QIZTruxt2rQ

End of Presentation

http://passyworldofmathematics.com

Visit our site for Free Mathematics PowerPoints