The Exponential Curve
Before we go further, there is a need to understand the term "exponential" so that the formulae and graphs presented in this text will be better understood.
The shape of exponential curves encodes deep mathematical properties that recur in a wide range of physical situations. An exponential curve is one that is everywhere equal to, or at least proportional to, its own slope. The exponential function is one of the most elegant mathematical relationships known to humankind, because an exponential curve can represent part of a sine wave, and physical systems which display exponential behavior may also display periodic sinusoidal behavior. This is important to the present discussion, since the exponential curves that are being presented could easily be the initial sweep of a sine wave curve, if the universe is cyclically undergoing expansion followed by contraction. The sine wave differs from an exponential curve in that it periodically and regularly goes up and down:
Whereas the exponential curve continuously always rises faster and faster or falls slower and slower:.25
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