The term exponential growth describes an observed effect in some basic technology, where performance per dollar multiplies over time.
In practice, exponential growth is seldom sustained indefinitely and usually ceases when some bounding condition, determined by physics or mathematics, is encountered, or when research and development funding collapses due to shifts in a commercial market-place or government funding priorities.
Unlike laws in hard sciences, which are immutable, exponential growth laws may collapse at any time if the social conditions producing them change.
In recent decades, the sustained exponential growth in digital technologies used for information-gathering, processing, storage, and distribution shows that the market for consumer and industrial digital equipment has yet to saturate, and key physics bounds have yet to be encountered.
If one knows tumor volume at two moments, one can calculate, using the exponential growth equations, a fixed number that everyone agrees is the doubling time.
Taking the final diameter of 6 cm and using the exponential growth equation, the initial diameter of the tumor was between 0.
By regression analysis using the exponential growth equation, the answer is 0.
But now, instead of taking exponential growth of the community as given, assume (following Tamiya's suggestion) that its growth can be attributed to the power of its literature to attract new authors.
The solution to the pair of equations (1) is given by the following exponential growth equations for the scientific community and its literature: (2) S = [S.
Such resilience of exponential growth to the underlying explanatory account of it would appear to be a special case of a more general resilience property of the exponential and other informetric distributions investigated in depth by Bookstein (1990, p.