Why Exponents are Important


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Uses of Exponents in the everyday world.

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Why Exponents are Important

  1. 1. Image Sources: http://4.bp.blogspot.com and http://img.ehowcdn.com
  2. 2. Power of 2 exponents are the basis of all computing which is done in “Binary” or base 2 numbers like these..
  3. 3. 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
  4. 4. Image Source: http://www.singularity.com
  5. 5. 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 Image Source: http://m5.paperblog.com
  6. 6. 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. Image Sources: http://www.marketoracle.co.uk and http://www.moneyguideindia.com
  7. 7. 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 Image Source: http://backtomyroots.wordpress.com
  8. 8. 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? Image Source: http://2.bp.blogspot.com
  9. 9. 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
  10. 10. 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.
  11. 11. 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.
  12. 12. 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.
  13. 13. 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.
  14. 14. Image Source: http://www.zeusbox.com In an uncontrolled Nuclear Explosion, Energy increases at an Exponential Rate as per Einstein’s Equation: E = mc2 .
  15. 15. 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.
  16. 16. 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 drop down reasonably fast at first, but then get slower and slower.
  17. 17. 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.
  18. 18. 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.
  19. 19. Image Source: www.union.ic.ac.uk 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)
  20. 20. Image Source: http://www.regentsprep.org
  21. 21. 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.
  22. 22. 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.
  23. 23. 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.
  24. 24. 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.
  25. 25. 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.
  26. 26. The following music video has had over 850,000 views on YouTube and is quite an amazing Production! http://www.youtube.com/watch?v=QIZTruxt2rQ
  27. 27. http://passyworldofmathematics.com Visit our site for Free Mathematics PowerPoints