When the scale factor depends exponentially on time, the scale factor goes to zero when time t goes to minus infinity. |
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The most common varieties are even vibration and damped vibration, according as the amplitude remains constant or it is decreasing exponentially. |
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Imagine tossing a coin until it lands heads-up, and suppose that the payoff grows exponentially according to the number of tosses you make. |
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The consumption per microprocessor increases while the number of microprocessors in use exponentially grows. |
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We have to point out that only numbers can increase exponentially and infinitely. |
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After all the winery's profits are exponentially greater with direct shipping. |
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The hassle factor goes up exponentially when you have to swage primer pockets and keep that brass separate. |
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The estimates for waiting times are not quantitatively reliable because they depend exponentially on imprecisely known quantities. |
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Most transient signals, which are exponentially damped sinusoids, cannot be wavelet basis functions because of their nonzero mean. |
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The burden could grow exponentially as the female participation rate in paid employment escalates. |
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With a single worm capable of laying 900 eggs a year, his worms began multiplying exponentially. |
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I could feel this slap-happy punch-drunk idiot grin appear on my face, widening exponentially. |
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The intensity of the evanescent wave created at the bottom of the flow cell decays exponentially with the distance from the slide's surface. |
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In contrast, an exponentially growing population has a smooth unimodal distribution approaching a Poisson distribution. |
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Basically, it's the idea that crime expands exponentially when small crimes go unpunished. |
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There is something vertiginously sublime about contemplating timescales that are exponentially longer than our own lives. |
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Investing capitalists came to feel that their wealth could go on expanding almost exponentially forever. |
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Conductance declined exponentially with applied pressure for both roots and stems. |
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The use of cellular phones and other wireless devices has been rising exponentially. |
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It measures the rate at which small disturbances explode exponentially in time. |
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The dye level for ventral bundles also rose initially to a maximum value, but dropped exponentially to a non-zero final value. |
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All beer heads decay exponentially with time, with most taking around three minutes to decay almost completely. |
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I think things can get magnified exponentially when you have two celebrities in a situation like this. |
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Medical websites have multiplied exponentially over the past several years. |
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How much longer can we exponentially expand our demand for energy and resources? |
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The credit default swap market, which enables investors to hedge the risk of default by individual borrowers, is increasing exponentially. |
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Rather than ameliorating his problems, however, these gadgets multiplied his frustrations exponentially. |
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Samples of 2.5x10 cells were also plated from exponentially growing cultures as control samples. |
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The turnover and employment figures rise exponentially when ancillary activities such as taxis and various contractor-suppliers are factored in. |
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Cosmetic surgery, the last resort of those who cannot hold on to their youth and beauty through diet and exercise, is expanding exponentially. |
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These developments were the beginning of the technology which has grown exponentially towards its modern explosion. |
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Franks was one of the founders of the scientific study of ethnography and increased the Museum's collections in that area exponentially. |
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The range of products is expanding just as exponentially as the means of operation. |
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In addition to exponentially increasing certain animal populations, the process of domestication has changed the very nature of its subjects. |
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Note that this is exponentially worse than the Manning Henkel problem, since there are not two but four dissyllables to conjure with. |
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Yet the biggest banks continue their practices and the sums of dirty money grow exponentially. |
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Our technological advances have increased exponentially over a few centuries, but our intercommunity and interracial skills have improved little. |
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Constant customer input helps provide an exponentially clearer picture of what kind of software designers need. |
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While revenues for Internet companies can grow exponentially, operating costs tend to grow linearly. |
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Mercenaries had grown exponentially, and trade routes were risky, the merchant ships pillaged. |
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The benefit increases exponentially when a higher priority is placed on the additional procurement of equipment for the Army Reserve. |
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The use of illegal drugs like marijuana, cocaine and heroin has increased exponentially, most dramatically among the young. |
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However, observations of the High Street late at night indicate the noise, filth and anti-social behaviour increase exponentially with the hour. |
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Therefore, the wear rate of rhino teeth, in terms of crown height, may decrease exponentially with age. |
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The size of neuron clusters that we have successfully recreated in terms of functional equivalence is also scaling up exponentially. |
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With all that silicon and increasingly-programmable APIs, low-level GPU programming is growing exponentially more intricate. |
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In de Sitter space the universe expands exponentially, which is the basis of the inflationary model of the universe. |
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The numbers of people active in the arts will grow exponentially as baby boomers retire. |
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The harvest of mantas in eastern Indonesia has increased exponentially in just a few years. |
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First, the evanescent field decays exponentially at the sensor surface. |
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Adding guns to that often alcohol-fueled mix exponentially increases the potential for avoidable tragedy. |
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Observations of change over the past century indicate that technology is evolving exponentially, which means change is accelerating or the rate of change is increasing. |
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Meanwhile, however, as they cleared the land and created and improved watering places for livestock, the settlers enabled the roos to multiply exponentially. |
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But as her wealth has grown exponentially, so has her reclusiveness. |
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Appliances such as refrigerators and stoves have increased exponentially. |
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This time, instead of dispersing the crowd, the police response swelled its ranks exponentially. |
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As the size of your string grows linearly larger, the difference between the significance of the most significant bit and the least significant bit grows exponentially larger. |
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That was in 2006 in Georgia, but in 2009, the project moved to New York and exponentially grew across the globe. |
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And if those consequences result in exponentially higher Brotherhood casualties than army casualties, then so be it. |
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What if we missed means to better, exponentially better, exploit our military supremacy? |
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Even the simple task of grasping an object is exponentially more difficult in a pressure suit. |
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I got used to drinking far less, which exponentially increased my energy for writing. |
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This time around, the failures and the mergers have been exponentially larger, as have the headlines about them around the world. |
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You can hear every footstep, which detracts from the experience exponentially. |
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Over the past thirty years, the movement has expanded exponentially to include emphases on nutrition, physical exercise and various body therapy approaches, including Rolfing. |
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The case also galvanized the gay-rights movement, which grew exponentially in its wake. |
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But alas, the mercenariness prevalent in our game will ensure that the high turnover of personnel at the Jags will rise exponentially with the club's success. |
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But new trawling technologies developed in Norway are poised to multiply the annual krill harvest exponentially. |
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Information technology continues to improve exponentially, and this progress bleeds over into adjacent fields such as genetics, robotics and nanotechnology. |
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Specifically, cell viability decreases exponentially with energy density. |
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As the day progressed, it seemed the misinformation on the internet was growing exponentially spurious by the minute. |
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What impresses me is that if you look at the subatomic level, or the quantum level, what you find is that the information processing power of nature goes up exponentially. |
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The concentration of CFCs in the atmosphere has increased almost exponentially since the 1930s but different chlorofluorocarbons have been released at known different rates. |
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The evolution of a classically chaotic Hamiltonian system is characterized by a computational complexity that increases exponentially with time elapsed. |
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The number of steps that are necessary to factorize a large number using all known algorithms increases exponentially with the size of the number. |
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The Internet will also help drive economies as it increases exponentially the ease, speed, and inexpensiveness with which information can be collected. |
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Data storage needs are increasing exponentially for most organizations. |
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The monsters in Carpenter's film become exponentially less and less human. |
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First, the human population is continuing to rise exponentially. |
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This means that the velocity of this particle decays exponentially to zero as time progresses. |
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During the period of slavery, the populations of Europe and the Americas grew exponentially, while the population of Africa remained stagnant. |
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Viewership increased exponentially from the 1960s until the end of the century. |
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However, our seminar registrations via the web have increased exponentially each year. |
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According to the other side, the numbers were exponentially greater. |
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When exposed inner tissue becomes infected, even small populations of the food-poisoning agent can grow exponentially, his data show. |
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It is clear from the beginning, and compared with laying new fiber or a new head end it is exponentially less costly. |
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But every known algorithm for this problem requires a number of steps that increases exponentially as n increases. |
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Since achieving independence as a result of the partition of India, the urbanisation has increased exponentially, with several different causes. |
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They called the program Team River Runner, and their kayaking family soon grew exponentially. |
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But Julia set a standard for far more than a genre that has grown exponentially ever since. |
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Phillip Hammond, the UK's foreign secretary, chaired a meeting on Wednesday and said the virus is not growing exponentially and is containable. |
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Offshore oil and gas has exponentially increasing cost as water depth increases. |
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During the 1950s, Dutch immigration to South Africa began to increase exponentially for the first time in over a hundred years. |
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The population of the jellyfish grew exponentially and, by 1988, it was wreaking havoc upon the local fishing industry. |
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After this elastic phase, uplift proceeded by slow viscous flow so the rate of uplift decreased exponentially after that. |
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As a result of these policies the Philippine population increased exponentially. |
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Steamboat traffic including passenger and freight business grew exponentially in the decades before the Civil War. |
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Oscillatory motion is highest at the surface and diminishes exponentially with depth. |
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Whilst this seems like an incredibly low level of migration, the flow on effect from that audience sharing their experience will increase the result exponentially. |
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Therefore, if absorption causes an attenuation of the oscillation amplitude, the temperature must decrease exponentially with increasing thickness. |
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The exponentially modified Gaussian function is a reliable generalization that accounts for skewness in the peak shape since it is characterized by a non-zero third moment. |
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While considering time-varying demands, inventory modellers usually take the demand to be either linearly dependent or exponentially dependent upon time. |
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With awareness of the goji and wolfberry names growing exponentially, now is a good time to add wolfberry growing to diversify and add to farm income. |
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Rating agencies also grew in size and profitability as the number of issuers accessing the debt markets grew exponentially, both in the United States and abroad. |
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They increased exponentially through time until coming to saturation. |
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Such a search in the case of Rush Hour takes an amount of memory that increases algebraically with grid size, but the time required may increase exponentially. |
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The results of the study show that the carotid plaque area grew with age after 40, but increased exponentially with the number of years of smoking and egg yolk eating. |
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As demand for the new 2015 Maserati Ghibli is expected to grow exponentially over the coming year, this dealership has elected to diversify its Ghibli lineup. |
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It makes felicitous use of repeated chord patterns and ostinati and long vocal lines that grow exponentially towards a sense of wondrous fulfilment. |
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