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Why Exponent Powers are Important


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Exponents in the Real World

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Why Exponent Powers are Important

  1. 1. Image Sources: and
  2. 2. Computer Games use "Game Physics Engines" whichare low level programs inside the game to calculate themovement, interactions, and the geometry involved withthe game.These programs use lots of Algebra formulas in theirAlgorithms, and many of these formulas involve multiplyingpowers terms containing exponents.If the mathematics isnt correct inthe game engine, then the gameis not going to play at all like wewould expect it to.Image Source:
  3. 3. If 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 etcSpread 1 + 10 + 100 + 1000 + 10 000Powers 100 101 102 103 104Spread = 10LevelImage Source:
  4. 4. Money 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: and
  5. 5. If we have One Person and they have 4 children, and theneach of these children have 4 children, and so on, we get thefollowing Exponential Population Growth.Generation 0 1 2 3 4Children 1 4 16 64 216Powers Values (20)2(21)2(22)2(23)2(24)2Rule: (2Generation)2Children 1 4 16 64 216Image Source:
  6. 6. The 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:
  7. 7. With World’s rapidly growing population in recent years, FossilFuel use for Industry and Transportation has gone “through theroof”. (Eg. A Huge Exponential Increase in fuel consumption).Image Source:
  8. 8. Image Sources: and http://www.captees.comAt first only a few people had smart phones, then within only afew years, it seems that everybody has an iPhone or similar.Eg. The Growth in Smart Phone usage has been Exponential.
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  10. 10. Image Sources: and Card Debt was growing exponentially, until the GlobalFinancial Crisis dramatically slowed down consumer spending.
  11. 11. Image Sources: and http://farm6.staticflickr.comOnce Bacteria and Mould start growing on food that is notrefrigerated, it reaches harmful levels very quickly.
  12. 12. Image Source: such as Flus, and HIV AIDS can spread at ExponentialRates causing Epidemics affecting millions of people.
  13. 13. Image Source: http://www.zeusbox.comIn an uncontrolled Nuclear Explosion, Energy increases atan Exponential Rate as per Einstein’s Equation: E = mc2.
  14. 14. Image Sources: http://pixabay.comStraight Line graphs represent steady increases, but ExponentialCurve Graphs show growth happening at a faster and faster rate.
  15. 15. Image Source: http://letsmakerobots.comThere is also Exponential Decrease, or “Decay”, which occurs whenwe raise Fractions to Powers. In this type of decrease, things dropdown reasonably fast at first, but then get slower and slower.
  16. 16. Image Sources: and volume of sound decreases in a 1 / Distance x Distance, or1 / d2, or d-2relationship. Move 4 times further away, and thesound 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 todrop down to complete silence.
  17. 17. Image Sources: and http://italy.techinlifes.comThe light intensity from a Projector, or detected by a Camera,also follows the Inverse Square of a 1 / d2type relationship.
  18. 18. Image Source: 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 5Players 64 32 16 8 4 2Fraction 64/(20) 64/(21) 64/(22) 64/(23) 64/(24) 64/(25)
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  20. 20. Image Source: and http://www.science20.comHigh Level Radioactive Waste (HLW), from Nuclear Power Plantstakes thousands of years to reduce down to a safe level.
  21. 21. Image Source: http://lh3.googleusercontent.comThe “Richter Scale” quantifies the amount of seismic energy, (asthe Indexes of Powers of 10), that is released by an earthquake.
  22. 22. Image Source: http://online.wsj.comThe pH scale also uses Power of 10 Exponents, for how Acidic orAlkaline a substance is. Public Swimming Pools maintain a pHbetween 7.0 and 7.4 to provide the best possible comfort levelsfor the public, as well to ensure effective chlorine action.
  23. 23. Image Source: http://nerdsoftheroundtable.wordpress.comPowers of 10 Exponents, (called Scientific Notation), are used tospecify very large amounts, such as the distance between starsand Planets. Earth to Moon Distance is about 4 x 105km.
  24. 24. Image Source: http://www.soest.hawaii.eduNegative Powers of 10 Exponents, (called Scientific Notation), areused to specify very small decimal amounts, such as the distancebetween Silicon atoms in a Silicon Crystal which is 2.35 x 10-10m.
  25. 25. http://passyworldofmathematics.comVisit our site for Free Mathematics PowerPoints