Exponents, Index Numbers, Powers, and Indices are used in lots of parts of our modern technological world.
Exponents are used in Computer Game Physics, pH and Richter Measuring Scales, Science, Engineering, Economics, Accounting, Finance, and many other disciplines.
Exponential Growth is a critically important aspect of Finance, Demographics, Biology, Economics, Resources, Electronics and many other areas.
Exponential Decay is associated with Light, Sound, Sporting Fixtures, Dangerous Chemicals, and Radioactive Waste.
People who use Exponents are Economists, Bankers, Financial Advisors, Insurance Risk Assessors, Biologists, Engineers, Computer Programmers, Chemists, Physicists, Geographers, Sound Engineers, Statisticians, Mathematicians, Geologists and many other professions.
In this lesson we show several Real Life uses of Exponents, as well as their impact on our understanding of the modern world around us.
Exponents are fundamental, especially in Base 2 and Base 16, as well as in Physics and Electronics formulas involved in Computing.
There has been an Exponential increase in the speed and power of computers over recent years, and by around 2030 computing power is predicted to match that of the human brain.
Exponents are critcally important in modern Internet based Sales and Marketing,
Exponents are important in Investing and Finance.
Compound Interest also works against people with a Credit Card debt they do not pay off, because the debt grows faster and faster each billing period and can quickly become out of control.
Exponents are the basis of “Demographics” (Population Growth)
The World’s Population is increasing at an extraordinary rate, especially in the devloping regions of Africa, India, and China.
With massive Population Growth comes massive use of Fossil Fuels for Industry, Heating, Electricity, and Transportation.
Over the last few years there has been massive exponential increases in mobile phone usage and market penetration.
Consumer Credit Debt has increased over recent years to record high levels.
Exponents are also part of Food Technology and Microbiology.
Virus Illness, (as well as many email and computer viruses), can spread at ever increasing rates causing major widespread infected areas.
This happens the same way that Viral Marketing branches out in ever increasingly wide branches of more and more people passing something onto more and more other people.
In explosions we get an uncontrolled massively increasing output of energy and force within a very short time period.
Picture this as a very steep exponential graph, compared to a burning match giving out energy in a fairly flat straight line graph.
The situations we have been considering so far involve “Exponential Growth”.
The equations for graphs of these situations contain exponents, and this results in the graph starting off slow, but then increasing very rapidly.
Eg. Think of Square Numbers and how they quickly get bigger and bigger:
1 4 9 16 25 36 49 64 81 100 121 132 etc
It only takes us nine square numbers to reach 100.
Exponential Growth situations when graphed look like the diagram below.
The opposite of “Exponential Growth”, is when we apply exponents to fractions which results in “Exponential Decay”.
Using negative power values results in fractions, and when these fractions have exponents applied to them we get “Decay”.
In a “Decay” process the amount involved drops off fairly quickly at the start, but then the drop off becomes slower and slower.
A typical Exponential Decay graph looks like this:
Making an Exponential Decay Graph
A fun way to make an Exponential decay graph is to take a pack of M&M’s or Skittles and keep pouring them out of a cup, but each time removing any candies which land with the letter side showing.
This should produce the required graph.
There is a great set of instructions on how to do this at the following link:
Exponential Decay – Real Life Examples
Some examples of Exponential Decay in the real world are the following.
Exponential Decay and Half Life
Many harmful materials, especially radioactive waste, take a very long time to break down to safe levels in the environment.
This is because these materials undergo exponential decay, and even a small amount of the material still remaining can be harmful.
The Richter Scale is used to measure how powerful earthquakes are.
The actual energy from each quake is a power of 10, but on the scale we simply take the index value of 1, 2, 3, 4, etc rather than the full exponent quantity.
This means that a Richter Scale 6 earthquake is actually 10 times stronger than a Richter Scale 5 quake. (Eg. 1000000 vs 100000).
Likewise, a Richter Scale 7 earthquake is actually 100 times stronger than a Richter Scale 5 quake. (Eg. 10000000 vs 100000).
The pH Scale for measuring the Acidity of materials is also created by taking the Power Values from measured powers of 10 acid concentration values.
Exponents and Scientific Notation
Very large numbers, like the distance between planets, or the population of countries, are expressed using powers of 10 in a format called “Scientific Notation”.
Scientific Notation is also used for expressing very small decimal values like the size of flu virus molecules, or the distance between atoms in a crystal structure.
Online Presentation on Exponents in the Real World
An online presentation of this lesson is available on SlideShare at the following Link:
Music Video About Exponents
The following music video all about Exponents, is possibly the most successful Math video ever uploaded to YouTube.
It has currently had over 850,000 views on YouTube and is quite an amazing Production!
Well worthy of viewing by anyone learning Indices and Exponents.
Basic Indices and Exponents
Dividing Algebra Expressions
Dividing Exponents Using Subtraction Rule
Expanding Exponents Using Power of Power Rule
Expanding Exponent Products Rule
Expanding Exponent Quotients Rule
Zero and Negative Exponents
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