exponential decay

I remember when I was a small child, and I looked around at a world that seemed to move smoothly, to operate freely, and to draw upon my curiosity daily. My father who wore many hats as I grew up was a bookkeeper who took the value of money seriously. He prided himself in taking care of his possessions and keeping things running like a well-oiled machine. My mother would pinch pennies and fed a large family on a very modest income. My parents instilled in me the need to be observant, to know the world around me intimately, and to understand its operation.

            Math was extremely important to my Dad, and he translated his passion to me and I now hunger to see the solution to the equation. In this day, as we look around we see an economy in danger. We realize that there is not much left to our national financial security and we are forced to wonder, “What can be done?”

            Because of this class especially, I have begun to think using the different sequences and equations we have used to ascertain the financial state of the world around us. We are in times of economic decay. What can be done to salvage our world?

            One of the things we can employ is formulas for exponential decay. This concept does not necessarily have to relate to money alone. It may also be used in the area of nature (bacteria, animal population, and wetland water levels). We can relate it to bank accounts, yes. We may also relate it to viruses such as AIDS, radioactive materials, temperatures, and credit payments.

            According to thefreedictionary.com the definition of exponential decay is “a decrease that follows an exponential function”. In laymen’s terms, it is the decline of numbers in an exponential pattern that follows a ratio of decrease at an exponential rate. The rate of change remains constant. It would increase as time wore on due to its exponential value.

            A quantity is said to be subject to exponential rates of decay if it decreases at a rate proportional to its value. If the decay quantity holds a relative exponential value it can be determined how long it will take for complete dissolution. The rate of change remains constant and can therefore be followed actively, predicted and perhaps augmented or stopped altogether.

            The reverse of this approach would be named exponential growth and would have the opposite exponential effect. Again, being able to be tracked and predicted through careful mathematic calculation.

            National Geographic can use exponential decay formulas to determine the water decline in wetland preservation areas, the animals that are endangered or close to becoming endangered. This type of mathematical equation can be employed to allow for the salvage of an entire species.

            Of course the rate of decay is directly proportionate to the amount present. Therefore, as in any mathematical or scientific approach, things must be accounted for accurately in the beginning of the process in order for the equation to function as designed. Careful observation and numbering would be highly necessary.

            As we watch the world around us decay we can sit back and allow it to happen or we can become an active role in preventing the extinction of species, the propagation of viruses that could be calculated and maintained. There is so much in the mathematical world around us that can be ordered, efficiently approached, and filtered through equations and sequences that would help us find cosmic rhythm in the surrounding counterparts.

            After learning about fractal geometry, the Golden Ration, the Fibonacci sequence and now exponential decay, I realize where higher math minds could be employed to help us calculate the augmentations necessary to resume order to the world around us.

            Whether we are attacking the concept of bacterial widespread, the mass extinction of more than one species of animal or plant life, the depletion of our natural water supply, the exponential decay formula can come into use and aid us in changing our world around us.

            One day, I hope to have children, and I would hope that they too could be afforded the privilege of looking around them at the world outside their classroom, the spectrum outside their toy box and find that the world is ordered, mathematical, and structured at such a high rhythmic process that only some minds are able to attain the spaces needed to maintain formulaic approaches. But, it can be done. This is the world that I would like to bring my children in to. This is the world that I believe can exist.

            I have always loved math. I have always loved music. I have always loved nature. Seeing the algebraic and formulaic equation represented between the biological worlds around me give me hope that we will find a solution to the 2012 confusion. I believe in the possibility of a brighter tomorrow. I intend to be one of the ones who rise up to make a change on this planet before it is too late. The more I learn the more exponential potential I obtain.

            Thank you for the thoughts this class has placed in my ever seeking knowledge brain.

References:

Thefreedictionary.com

Mathwords.com

Ucsd.edu

Regentsprep.org