Having improved itself it would become better at improving itself, potentially leading to an exponential increase in intelligence.

The need for a labor force to meet the growing demands of sugar cane cultivation led to an exponential increase in the importation of slaves over the following two decades.

The exponential function is used to model a relationship in which a constant change in the independent variable gives the same proportional change ( i. e. percentage increase or decrease ) in the dependent variable.

However, the exponential power increase cannot continue for long since k decreases when the amount of fission material that is left decreases ( i. e. it is consumed by fissions ).

They direct replication towards each other – the extension of one primer by polymerase then becomes the template for the other, leading to an exponential increase in the target segment.

Since that fuel must itself be accelerated, this results in an approximately exponential increase in mass as a function of velocity change at non-relativistic speeds, asymptotically tending to infinity as it approaches the speed of light.

That is, where the number of elements which are exposed to mutation is large there is often an exponential increase in search space size.

This process results in production of enough DNA to be visible on agarose or polyacrylamide gels ; only small amounts of DNA are needed for amplification because in this way thermocycling creates an exponential increase in the replicated segment.

The exponential increase in construction activity is a part of the Strategy for Academic Development at UCI through 2015, a master plan that outlines the vision of making UCI a first-choice university for college applicants nationwide.

Market factors include the exponential increase in value of diamonds as weight increases, referred to as weight retention, and the popularity of certain shapes amongst consumers.

where is the starting frequency ( at ), and is the rate of exponential increase in frequency.

Because of the geometric relationship, the Doppler shifted geometric chirp will effectively start at a different frequency ( multiplied by a constant ), but follow the same pattern of exponential frequency increase, so the end of the original wave, for instance, will still overlap perfectly with the beginning of the reflected wave, and the magnitude of the correlation will be high for that section of the wave.

Five variables were examined in the original model, on the assumptions that exponential growth accurately described their patterns of increase, and that the ability of technology to increase the availability of resources grows only linearly.

There exist transformations into CNF that avoid an exponential increase in size by preserving satisfiability rather than equivalence.

In the early 1980s, during the implementation of mandatory reporting laws there was an exponential increase in child protection investigations in America, Britain and other developed countries and an increased public awareness of child abuse.

Climbers started visiting the area as early as the 1950s and 60s but it wasn't until the 80s that the area really got " discovered " and was publicized ; with that of course came an exponential increase in route development.

Subsequent to the Cretaceous – Paleogene extinction event that eliminated the dinosaurs about 65. 5 Ma ago, terrestrial mammals underwent a nearly exponential increase in body size as they diversified to occupy the ecological niches left vacant.

However, when considered from the standpoint of rate of size increase per generation, the exponential increase is found to have continued until the appearance of Indricotherium 30 Ma ago.

Each unit increase on the logarithmic scale thus represents an exponential increase in the underlying quantity for the given base ( 10, in this case ).

Various power-ups, numerous in the first level but increasingly rare afterwards, permit an exponential increase of the spacecraft's seven different weapons ( Guns, Buildup, Side shots, Homing missiles, Plasma, Magma, Laserbeam ).

The rise of the Internet in the 1990s and 2000s saw an exponential increase in the production of independent animation.

An exponential increase was noted during the period of the current AIDS epidemic.

Unless certain countervailing possibilities are available, the exponential growth of capital out-paces the growth in labor productivity, so the profits of economic activity have to be shared out more thinly among capitals, i. e., at a lower profit rate.

This coupling of nutrients and phytoplankton promotes exponential increases in photosynthetic activity, and, thus, primary production.

If we define the function f ( n ) = A ( n, n ), which increases both m and n at the same time, we have a function of one variable that dwarfs every primitive recursive function, including very fast-growing functions such as the exponential function, the factorial function, multi-and superfactorial functions, and even functions defined using Knuth's up-arrow notation ( except when the indexed up-arrow is used ).

The exponential time hypothesis is that no algorithm can solve 3-Sat in time.

In physical cosmology, cosmic inflation, cosmological inflation or just inflation is the theorized extremely rapid exponential expansion of the early universe by a factor of at least 10 < sup > 78 </ sup > in volume, driven by a negative-pressure vacuum energy density.

In category theory, currying can be found in the universal property of an exponential object, which gives rise to the following adjunction in cartesian closed categories: There is a natural isomorphism between the morphisms from a binary product and the morphisms to an exponential object.

The result is in fact an exponential growth, thus giving rise to explosive increases in reaction rates, and indeed to chemical explosions themselves.

If is a constant, the solution is particularly simple, and describes, e. g., if, the exponential decay of radioactive material at the macroscopic level.

While the technique extends to higher dimension ( as proved by Edelsbrunner and Shah ), the runtime can be exponential in the dimension even if the final Delaunay triangulation is small.

The most widely used method of discounting is exponential discounting, which values future cash flows as " how much money would have to be invested currently, at a given rate of return, to yield the cash flow in future.

For other initial conditions, the equation of motion is given by the exponential of a matrix: for an initial point x < sub > 0 </ sub >,

If a Diophantine equation has as an additional variable or variables occurring as exponents, it is an exponential Diophantine equation.

Euler's formula, named after Leonhard Euler, is a mathematical formula in complex analysis that establishes the deep relationship between the trigonometric functions and the complex exponential function.

This complex exponential function is sometimes denoted The formula is still valid if x is a complex number, and so some authors refer to the more general complex version as Euler's formula.

The original proof is based on the Taylor series expansions of the exponential function e < sup > z </ sup > ( where z is a complex number ) and of sin x and cos x for real numbers x ( see below ).

The reason for this is that the complex exponential is the eigenfunction of differentiation.

Note that this derivation does assume that ƒ ( x ) is sufficiently differentiable and well-behaved ; specifically, that ƒ may be approximated by polynomials ; equivalently, that ƒ is a real analytic function of exponential type.

This is the essentially the reason for the restriction to exponential type of less than 2π: the function sin ( 2πnz ) grows faster than e < sup > 2π | z |</ sup > along the imaginary axis!

In mathematics, the exponential function is the function e < sup > x </ sup >, where e is the number ( approximately 2. 718281828 ) such that the function e < sup > x </ sup > is its own derivative.