1952:
608:
688:
2836:
255:
33:
2595:
2916:. The king asked what he would like in return for his gift and the courtier surprised the king by asking for one grain of rice on the first square, two grains on the second, four grains on the third, and so on. The king readily agreed and asked for the rice to be brought. All went well at first, but the requirement for
1951:
325:
into two daughter organisms, who then each split to form four, who split to form eight, and so on. Because exponential growth indicates constant growth rate, it is frequently assumed that exponentially growing cells are at a steady-state. However, cells can grow exponentially at a constant rate while
544:
will require 40 seconds. This kind of algorithm typically becomes unusable at very small problem sizes, often between 30 and 100 items (most computer algorithms need to be able to solve much larger problems, up to tens of thousands or even millions of items in reasonable times, something that would
217:
is often used to illustrate it. One bacterium splits itself into two, each of which splits itself resulting in four, then eight, 16, 32, and so on. The amount of increase keeps increasing because it is proportional to the ever-increasing number of bacteria. Growth like this is observed in real-life
431:
of the uranium), the production rate of neutrons and induced uranium fissions increases exponentially, in an uncontrolled reaction. "Due to the exponential rate of increase, at any point in the chain reaction 99% of the energy will have been released in the last 4.6 generations. It is a reasonable
2946:
French children are offered a riddle, which appears to be an aspect of exponential growth: "the apparent suddenness with which an exponentially growing quantity approaches a fixed limit". The riddle imagines a water lily plant growing in a pond. The plant doubles in size every day and, if left
2947:
alone, it would smother the pond in 30 days killing all the other living things in the water. Day after day, the plant's growth is small, so it is decided that it won't be a concern until it covers half of the pond. Which day will that be? The 29th day, leaving only one day to save the pond.
2370:
1045:
1606:
2849:
In reality, initial exponential growth is often not sustained forever. After some period, it will be slowed by external or environmental factors. For example, population growth may reach an upper limit due to resource limitations. In 1845, the
Belgian mathematician
2866:
Exponential growth models of physical phenomena only apply within limited regions, as unbounded growth is not physically realistic. Although growth may initially be exponential, the modelled phenomena will eventually enter a region in which previously ignored
1833:
1333:
769:
508:. (Under exponential growth, there are no singularities. The singularity here is a metaphor, meant to convey an unimaginable future. The link of this hypothetical concept with exponential growth is most vocally made by futurist
916:
519:, computer algorithms of exponential complexity require an exponentially increasing amount of resources (e.g. time, computer memory) for only a constant increase in problem size. So for an algorithm of time complexity
682:
2897:
Studies show that human beings have difficulty understanding exponential growth. Exponential growth bias is the tendency to underestimate compound growth processes. This bias can have financial implications as well.
1425:
2375:
1226:
2765:
598:
was uploaded to YouTube on 15 July 2012, reaching hundreds of thousands of viewers on the first day, millions on the twentieth day, and was cumulatively viewed by hundreds of millions in less than two months.
2147:
2590:{\displaystyle {\begin{aligned}{\frac {dx}{dt}}&=kx\\{\frac {dx}{x}}&=k\,dt\\\int _{x_{0}}^{x(t)}{\frac {dx}{x}}&=k\int _{0}^{t}\,dt\\\ln {\frac {x(t)}{x_{0}}}&=kt.\end{aligned}}}
700:
620:
1740:
242:
1230:
836:
196:
2287:
2049:
2653:
2237:
549:
do not help the situation much because doubling processor speed merely increases the feasible problem size by a constant. E.g. if a slow processor can solve problems of size
3532:
233:
Terms like "exponential growth" are sometimes incorrectly interpreted as "rapid growth". Indeed, something that grows exponentially can in fact be growing slowly at first.
1943:
594:, one person can forward the same content to many people simultaneously, who then spread it to even more people, and so on, causing rapid spread. For example, the video
2362:
226:. In real cases, initial exponential growth often does not last forever, instead slowing down eventually due to upper limits caused by external factors and turning into
885:
2821:
568:. So exponentially complex algorithms are most often impractical, and the search for more efficient algorithms is one of the central goals of computer science today.
321:
will increase exponentially until an essential nutrient is exhausted, so there is no more of that nutrient for more organisms to grow. Typically the first organism
378:
electrons also are accelerated, creating larger numbers of free electrons. The resulting exponential growth of electrons and ions may rapidly lead to complete
695:
447:
1137:
2702:
2938:" refers to the time when an exponentially growing influence is having a significant economic impact on an organization's overall business strategy.
615:
2776:
Growth rates may also be faster than exponential. In the most extreme case, when growth increases without bound in finite time, it is called
432:
approximation to think of the first 53 generations as a latency period leading up to the actual explosion, which only takes 3–4 generations."
2065:
1109:
If a species of bacteria doubles every ten minutes, starting out with only one bacterium, how many bacteria would be present after one hour?
3526:
2769:
There is a whole hierarchy of conceivable growth rates that are slower than exponential and faster than linear (in the long run). See
3560:
1040:{\displaystyle x(t+\tau )=a\cdot b^{\frac {t+\tau }{\tau }}=a\cdot b^{\frac {t}{\tau }}\cdot b^{\frac {\tau }{\tau }}=x(t)\cdot b\,.}
1904:
in the last formula is not a numerical division either, but converts a dimensionless number to the correct quantity including unit.
1737:, have a one-to-one connection given by the following equation (which can be derived by taking the natural logarithm of the above):
4125:
3112:
2875:
model) or other underlying assumptions of the exponential growth model, such as continuity or instantaneous feedback, break down.
1601:{\displaystyle x(t)=x_{0}\cdot e^{kt}=x_{0}\cdot e^{t/\tau }=x_{0}\cdot 2^{t/T}=x_{0}\cdot \left(1+{\frac {r}{100}}\right)^{t/p},}
3757:
2770:
487:
also show this type of growth resulting in high profits for a few initial investors and losses among great numbers of investors.
3334:
3307:
3261:
785:
139:
2246:
1961:
Graphs comparing doubling times and half lives of exponential growths (bold lines) and decay (faint lines), and their 70/
1958:
1418:
Thus the law of exponential growth can be written in different but mathematically equivalent forms, by using a different
272:
3668:
3632:
2600:
17:
4031:
3503:
3489:
3475:
3461:
3445:
3414:
3389:
294:
1372:
which can be expressed as the product of a number of units and a unit of time) represent the same growth rate, with
99:
If the constant of proportionality is negative, then the quantity decreases over time, and is said to be undergoing
3851:
3846:
3841:
3836:
3831:
3826:
3821:
3816:
3278:
2931:) on the 41st and there simply was not enough rice in the whole world for the final squares. (From Swirski, 2006)
2928:
2687:
In the long run, exponential growth of any kind will overtake linear growth of any kind (that is the basis of the
516:
84:
of time, that is, the variable representing time is the exponent (in contrast to other types of growth, such as
4140:
4135:
851:
276:
4066:
3946:
3709:
3553:
2935:
73:
3094:
64:
is a process that increases quantity over time at an ever-increasing rate. It occurs when the instantaneous
3951:
3941:
3881:
3724:
3719:
2907:
2240:
36:
The graph illustrates how exponential growth (green) surpasses both linear (red) and cubic (blue) growth.
3896:
3750:
3027:
2152:
1990:
3516:/ Ed. by M. G. Dmitriev and A. P. Petrov, pp. 367–9. Moscow: Russian State Social University, 2004.
2851:
1828:{\displaystyle k={\frac {1}{\tau }}={\frac {\ln 2}{T}}={\frac {\ln \left(1+{\frac {r}{100}}\right)}{p}}}
4041:
3032:
1655:
134:
goes on in discrete intervals (that is, at integer times 0, 1, 2, 3, ...), is
3482:
Of
Literature and Knowledge: Explorations in Narrative Thought Experiments, Evolution, and Game Theory
2912:
According to legend, vizier Sissa Ben Dahir presented an Indian King Sharim with a beautiful handmade
2187:
1970:
4026:
3891:
1672:
1393:
505:
4104:
3546:
3136:"Constant Growth Rate Can Be Supported by Decreasing Energy Flux and Increasing Aerobic Glycolysis"
1914:
3047:
2992:
2887:
318:
265:
65:
2325:
2155:. For example, if one wishes to empirically estimate the growth rate from intertemporal data on
1328:{\displaystyle x(1{\text{ hr}})=1\cdot 2^{(60{\text{ min}})/(10{\text{ min}})}=1\cdot 2^{6}=64.}
4145:
4099:
3994:
3743:
3678:
3642:
2883:
2688:
1651:
420:
412:
385:
81:
77:
4130:
4061:
4051:
3989:
3714:
3251:
3022:
2997:
2962:
2780:. In between exponential and hyperbolic growth lie more classes of growth behavior, like the
116:
2791:
1907:
A popular approximated method for calculating the doubling time from the growth rate is the
3452:
3450:
Meadows, Donella H., Dennis L. Meadows, Jørgen
Randers, and William W. Behrens III. (1972)
3435:
2839:
The J-shaped exponential growth (left, blue) and the S-shaped logistic growth (right, red).
2182:
379:
104:
3350:
Stango, Victor; Zinman, Jonathan (2009). "Exponential Growth Bias and
Household Finance".
2924:
th square demanded over a million grains on the 21st square, more than a million million (
8:
3936:
3012:
2972:
2957:
351:
764:{\displaystyle {\begin{aligned}a&=24\\b&={\frac {1}{2}}\\r&=5\end{aligned}}}
218:
activity or phenomena, such as the spread of virus infection, the growth of debt due to
3984:
3886:
3876:
3704:
3583:
3230:
3168:
3135:
3037:
2824:
93:
3901:
3499:
3485:
3471:
3457:
3441:
3410:
3385:
3363:
3330:
3303:
3257:
3173:
3155:
3042:
3017:
2868:
2777:
2676:
2665:
2160:
1369:
1101:
470:
435:
219:
100:
4086:
3906:
3856:
3623:
3359:
3192:
3163:
3147:
3067:
2977:
2879:
587:
509:
389:
363:
214:
89:
85:
3509:
4046:
3688:
3324:
3297:
3151:
3131:
2872:
2055:
1337:
After one hour, or six ten-minute intervals, there would be sixty-four bacteria.
591:
473:
at a constant interest rate provides exponential growth of the capital. See also
404:
393:
4076:
3967:
3866:
3598:
3593:
3569:
3510:
On the
Possible Reasons for the Hyperexponential Growth of the Earth Population
3072:
3062:
2982:
2855:
2844:
2781:
1419:
546:
501:
480:
400:
227:
1898:, but for uniformity this has been avoided here. In this case the division by
545:
be physically impossible with an exponential algorithm). Also, the effects of
460:
Economic growth is expressed in percentage terms, implying exponential growth.
4119:
4036:
3811:
3791:
3766:
3159:
3057:
2320:
1884:
for the (dimensionless) number of units of time rather than the time itself,
1681:
1353:
900:
595:
579:
322:
314:
4071:
3177:
2967:
607:
484:
338:
687:
677:{\displaystyle {\begin{aligned}a&=3\\b&=2\\r&=5\end{aligned}}}
4081:
4021:
3673:
3637:
2987:
583:
416:
223:
3871:
3652:
2913:
2692:
1908:
497:
474:
442:
can result in the exponential growth of the amplified signal, although
355:
279: in this section. Unsourced material may be challenged and removed.
241:
69:
48:
3527:
Growth in a Finite World – Sustainability and the
Exponential Function
1221:{\displaystyle x(t)=a\cdot b^{t/\tau }=1\cdot 2^{t/(10{\text{ min}})}}
3977:
3972:
3806:
3683:
3608:
3603:
3052:
2854:
first proposed a mathematical model of growth like this, called the "
2785:
2672:
2059:
1663:
1641:
443:
439:
2760:{\displaystyle \lim _{t\to \infty }{\frac {t^{\alpha }}{ae^{t}}}=0.}
254:
3911:
3647:
3613:
3588:
3207:
3002:
2835:
2151:
This allows an exponentially growing variable to be modeled with a
1409:
the growth rate is given by the dimensionless positive number
557:, then a processor twice as fast could only solve problems of size
419:
of neutron absorption exceeds the probability of neutron escape (a
415:
by adjacent uranium atoms, causing them to fission in turn. If the
371:
359:
334:
330:
3538:
3496:
Blueprint to a
Billion: 7 Essentials to Achieve Exponential Growth
3235:
3095:"Opinion | Stop Saying 'Exponential.' Sincerely, a Math Nerd"
341:
is available. Each infected person can infect multiple new people.
3801:
3007:
408:
397:
337:) typically will spread exponentially at first, if no artificial
3735:
4056:
3861:
3796:
2771:
Degree of a polynomial § Computed from the function values
27:
Growth of quantities at rate proportional to the current amount
32:
590:" as an analogy to the spread of viruses. With media such as
424:
245:
Bacteria exhibit exponential growth under optimal conditions.
3299:
Functions and Change: A Modeling
Approach to College Algebra
3326:
Population
Ecology: An Introduction to Computer Simulations
2367:
The differential equation is solved by direct integration:
428:
367:
1880:
is simply the number of units of time. Using the notation
366:
that it frees up additional electrons as it collides with
362:
becomes sufficiently accelerated by an externally applied
3786:
3279:"Gangnam Style vs Call Me Maybe: A Popularity Comparison"
3129:
438:
within the linear range of electrical or electroacoustic
3249:
1973:, hover over a graph to highlight it and its complement.
1627:
Parameters (negative in the case of exponential decay):
3433:
Meadows, Donella. Randers, Jorgen. Meadows, Dennis.
1650:; in finance it is also called the logarithmic return,
1644:(number of times per unit time) of growing by a factor
530:
requires 10 seconds to complete, and a problem of size
3533:
Dr. Albert
Bartlett: Arithmetic, Population and Energy
2142:{\displaystyle \log x(t)=\log x_{0}+t\cdot \log(1+r).}
586:, can spread in an exponential manner, often said to "
107:
of definition with equal intervals, it is also called
3514:
Mathematical Modeling of Social and Economic Dynamics
2794:
2705:
2603:
2373:
2328:
2249:
2190:
2068:
1993:
1978:
1917:
1743:
1428:
1397:
or 2), the growth rate is given by the non-zero time
1233:
1140:
919:
854:
788:
698:
618:
142:
3228:
3193:"Introduction to Nuclear Weapon Physics and Design"
3130:Slavov, Nikolai; Budnik, Bogdan A.; Schwab, David;
3296:Crauder, Bruce; Evans, Benny; Noell, Alan (2008).
2815:
2759:
2647:
2589:
2356:
2281:
2231:
2141:
2062:of both sides of the exponential growth equation:
2043:
1937:
1827:
1600:
1327:
1220:
1039:
879:
830:
763:
676:
190:
3295:
3213:
3113:"10 Scientific Words You're Probably Using Wrong"
122:The formula for exponential growth of a variable
80:, a quantity undergoing exponential growth is an
4117:
2707:
326:remodeling their metabolism and gene expression.
3375:
3373:
3123:
2289:saying that the change per instant of time of
3751:
3554:
3398:
3370:
3349:
537:requires 20 seconds, then a problem of size
3229:Ariel Cintrón-Arias (2014). "To Go Viral".
1422:. The most common forms are the following:
3758:
3744:
3561:
3547:
3302:. Houghton Mifflin Harcourt. p. 398.
2892:
3322:
3234:
3167:
2871:factors become significant (leading to a
2522:
2440:
1987:exhibits exponential growth according to
1670:is the time it takes to grow by a factor
1033:
873:
295:Learn how and when to remove this message
3409:. Chelsea Green Publishing. p. 21.
3407:The Limits to Growth: The 30-Year Update
2861:
2834:
2176:
686:
606:
240:
72:) of a quantity with respect to time is
31:
3404:
3379:
3276:
2901:
2657:In the above differential equation, if
831:{\displaystyle x(t)=a\cdot b^{t/\tau }}
76:to the quantity itself. Described as a
14:
4118:
3739:
3542:
3329:. John Wiley & Sons. p. 37.
3224:
3222:
3134:; van Oudenaarden, Alexander (2014).
2925:
2682:
1697:(a dimensionless number) in a period
572:
213:at time 0. The growth of a bacterial
3190:
3092:
2058:over time, as can be seen by taking
277:adding citations to reliable sources
248:
191:{\displaystyle x_{t}=x_{0}(1+r)^{t}}
3568:
3382:Capitalism: as if the world matters
3250:Karine Nahon; Jeff Hemsley (2013).
2675:variation of this growth model see
2282:{\displaystyle {\frac {dx}{dt}}=kx}
2044:{\displaystyle x(t)=x_{0}(1+r)^{t}}
491:
103:instead. In the case of a discrete
24:
3535:— streaming video and audio 58 min
3468:Capitalism as if the world matters
3219:
2830:
2717:
1979:Reformulation as log-linear growth
25:
4157:
4032:Indefinite and fictitious numbers
3765:
3520:
3384:. London: Earthscan. p. 49.
2648:{\displaystyle x(t)=x_{0}e^{kt}.}
1870:is the unit of time the quotient
893:is a positive growth factor, and
115:since the function values form a
3440:Chelsea Green Publishing, 2004.
3364:10.1111/j.1540-6261.2009.01518.x
2664:, then the quantity experiences
2297:is proportional to the value of
2232:{\displaystyle x(t)=x_{0}e^{kt}}
2051:, then the log (to any base) of
1950:
602:
253:
4126:Ordinary differential equations
3343:
3316:
3214:Crauder, Evans & Noell 2008
1688:is the time it takes to double.
1617:expresses the initial quantity
517:computational complexity theory
374:of the dielectric media. These
264:needs additional citations for
3456:. New York: University Books.
3289:
3270:
3243:
3184:
3105:
3086:
2810:
2798:
2714:
2613:
2607:
2551:
2545:
2477:
2471:
2338:
2332:
2200:
2194:
2133:
2121:
2084:
2078:
2032:
2019:
2003:
1997:
1652:continuously compounded return
1438:
1432:
1295:
1284:
1276:
1265:
1248:
1237:
1213:
1202:
1150:
1144:
1024:
1018:
935:
923:
864:
858:
798:
792:
778:depends exponentially on time
179:
166:
13:
1:
3947:Conway chained arrow notation
3710:Conway chained arrow notation
3079:
2941:
2936:second half of the chessboard
907:to increase by one factor of
3152:10.1016/j.celrep.2014.03.057
3093:Suri, Manil (4 March 2019).
2908:Wheat and chessboard problem
2241:linear differential equation
1938:{\displaystyle T\simeq 70/r}
454:
7:
3028:Law of accelerating returns
2950:
1067:has exponential growth. If
578:Internet contents, such as
236:
10:
4162:
4042:Largest known prime number
3662:Inverse for right argument
3427:
3380:Porritt, Jonathan (2005).
3033:List of exponential topics
2905:
2877:
2842:
2357:{\displaystyle x(0)=x_{0}}
464:
450:of the signal over others.
345:
307:
4095:
4027:Extended real number line
4007:
3960:
3942:Knuth's up-arrow notation
3929:
3920:
3773:
3720:Knuth's up-arrow notation
3697:
3661:
3622:
3576:
3405:Meadows, Donella (2004).
3195:. Nuclear Weapons Archive
2695:growth, that is, for all
880:{\displaystyle x(0)=a\,,}
506:technological singularity
88:). Exponential growth is
3952:Steinhaus–Moser notation
3725:Steinhaus–Moser notation
3323:Bernstein, Ruth (2003).
2852:Pierre François Verhulst
1403:. For any non-zero time
844:is the initial value of
56: Exponential growth
3484:. New York: Routledge.
3048:Malthusian growth model
2993:Combinatorial explosion
2893:Exponential growth bias
2888:Apparent infection rate
1969:approximations. In the
903:—the time required for
523:, if a problem of size
500:of computers. See also
446:effects may favor some
411:, each of which can be
3995:Fast-growing hierarchy
3352:The Journal of Finance
3256:. Polity. p. 16.
2884:Malthusian catastrophe
2840:
2823:, the diagonal of the
2817:
2816:{\displaystyle A(n,n)}
2761:
2689:Malthusian catastrophe
2649:
2591:
2358:
2283:
2233:
2143:
2045:
1939:
1829:
1602:
1362:and an amount of time
1329:
1222:
1041:
881:
832:
771:
765:
684:
678:
386:Nuclear chain reaction
246:
192:
58:
4141:Mathematical modeling
4136:Temporal exponentials
4052:Long and short scales
3990:Grzegorczyk hierarchy
3715:Grzegorczyk hierarchy
3438:: The 30-Year Update.
3023:Information explosion
2998:Exponential algorithm
2963:Albert Allen Bartlett
2878:Further information:
2862:Limitations of models
2838:
2818:
2762:
2650:
2592:
2359:
2284:
2234:
2177:Differential equation
2144:
2046:
1940:
1830:
1691:The percent increase
1603:
1391:not equal to 1 (e.g.
1330:
1223:
1111:The question implies
1042:
882:
833:
766:
690:
679:
610:
448:component frequencies
329:A virus (for example
244:
193:
117:geometric progression
35:
3508:Tsirel, S. V. 2004.
3453:The Limits to Growth
3436:The Limits to Growth
2902:Rice on a chessboard
2792:
2703:
2601:
2371:
2326:
2247:
2188:
2183:exponential function
2066:
1991:
1915:
1741:
1426:
1356:non-negative number
1231:
1138:
917:
852:
786:
696:
616:
388:(the concept behind
380:dielectric breakdown
273:improve this article
222:, and the spread of
140:
82:exponential function
4067:Orders of magnitude
3937:Scientific notation
3689:Super-logarithm (4)
3648:Root extraction (3)
3216:, pp. 314–315.
3132:Airoldi, Edoardo M.
3013:Hausdorff dimension
2973:Asymptotic notation
2958:Accelerating change
2521:
2481:
1894:can be replaced by
838:where the constant
611:exponential growth:
352:Avalanche breakdown
126:at the growth rate
41: Linear growth
3985:Ackermann function
3705:Ackermann function
3599:Exponentiation (3)
3594:Multiplication (2)
3498:, Wiley Dec 2005,
3494:Thomson, David G.
3470:, Earthscan 2005.
3099:The New York Times
3038:Logarithmic growth
2841:
2825:Ackermann function
2813:
2757:
2721:
2683:Other growth rates
2645:
2587:
2585:
2507:
2451:
2354:
2279:
2229:
2139:
2041:
1935:
1825:
1725:, and for a given
1598:
1325:
1218:
1037:
877:
828:
772:
761:
759:
691:exponential decay:
685:
674:
672:
573:Internet phenomena
407:produces multiple
247:
188:
94:logarithmic growth
62:Exponential growth
59:
18:Grow exponentially
4113:
4112:
4003:
4002:
3733:
3732:
3626:for left argument
3336:978-0-470-85148-7
3309:978-1-111-78502-4
3263:978-0-7456-7129-1
3191:Sublette, Carey.
3043:Logistic function
3018:Hyperbolic growth
2869:negative feedback
2778:hyperbolic growth
2749:
2706:
2691:) as well as any
2677:logistic function
2666:exponential decay
2565:
2495:
2428:
2396:
2268:
1823:
1812:
1779:
1758:
1656:force of interest
1574:
1370:physical quantity
1293:
1274:
1246:
1211:
1102:exponential decay
1009:
991:
967:
738:
564:in the same time
471:Compound interest
436:Positive feedback
358:material. A free
305:
304:
297:
220:compound interest
101:exponential decay
16:(Redirected from
4153:
3927:
3926:
3857:Eddington number
3802:Hundred thousand
3760:
3753:
3746:
3737:
3736:
3698:Related articles
3563:
3556:
3549:
3540:
3539:
3480:Swirski, Peter.
3421:
3420:
3402:
3396:
3395:
3377:
3368:
3367:
3358:(6): 2807–2849.
3347:
3341:
3340:
3320:
3314:
3313:
3293:
3287:
3286:
3277:YouTube (2012).
3274:
3268:
3267:
3247:
3241:
3240:
3238:
3226:
3217:
3211:
3205:
3204:
3202:
3200:
3188:
3182:
3181:
3171:
3127:
3121:
3120:
3109:
3103:
3102:
3090:
3068:Quadratic growth
2978:Bacterial growth
2927:
2923:
2919:
2880:Limits to Growth
2822:
2820:
2819:
2814:
2766:
2764:
2763:
2758:
2750:
2748:
2747:
2746:
2733:
2732:
2723:
2720:
2698:
2663:
2654:
2652:
2651:
2646:
2641:
2640:
2628:
2627:
2596:
2594:
2593:
2588:
2586:
2566:
2564:
2563:
2554:
2540:
2520:
2515:
2496:
2491:
2483:
2480:
2466:
2465:
2464:
2429:
2424:
2416:
2397:
2395:
2387:
2379:
2363:
2361:
2360:
2355:
2353:
2352:
2318:
2307:
2296:
2292:
2288:
2286:
2285:
2280:
2269:
2267:
2259:
2251:
2238:
2236:
2235:
2230:
2228:
2227:
2215:
2214:
2172:
2168:
2161:linearly regress
2158:
2153:log-linear model
2148:
2146:
2145:
2140:
2105:
2104:
2054:
2050:
2048:
2047:
2042:
2040:
2039:
2018:
2017:
1986:
1954:
1944:
1942:
1941:
1936:
1931:
1903:
1897:
1893:
1883:
1879:
1869:
1861:being infinite.
1860:
1854:
1848:
1841:
1834:
1832:
1831:
1826:
1824:
1819:
1818:
1814:
1813:
1805:
1785:
1780:
1775:
1764:
1759:
1751:
1736:
1730:
1724:
1718:
1712:
1702:
1696:
1649:
1639:
1623:
1616:
1607:
1605:
1604:
1599:
1594:
1593:
1589:
1580:
1576:
1575:
1567:
1550:
1549:
1537:
1536:
1532:
1516:
1515:
1503:
1502:
1498:
1482:
1481:
1469:
1468:
1453:
1452:
1414:
1408:
1402:
1390:
1385:. For any fixed
1384:
1378:proportional to
1377:
1367:
1361:
1351:
1334:
1332:
1331:
1326:
1318:
1317:
1299:
1298:
1294:
1291:
1283:
1275:
1272:
1247:
1244:
1227:
1225:
1224:
1219:
1217:
1216:
1212:
1209:
1201:
1179:
1178:
1174:
1131:
1124:
1117:
1099:
1095:
1087:
1080:
1073:
1066:
1062:
1055:
1046:
1044:
1043:
1038:
1011:
1010:
1002:
993:
992:
984:
969:
968:
963:
952:
912:
906:
898:
892:
886:
884:
883:
878:
847:
843:
837:
835:
834:
829:
827:
826:
822:
781:
777:
770:
768:
767:
762:
760:
739:
731:
683:
681:
680:
675:
673:
567:
563:
556:
552:
543:
536:
529:
522:
498:Processing power
492:Computer science
390:nuclear reactors
382:of the material.
364:electrical field
300:
293:
289:
286:
280:
257:
249:
212:
209:is the value of
208:
197:
195:
194:
189:
187:
186:
165:
164:
152:
151:
133:
129:
125:
109:geometric growth
86:quadratic growth
55:
46:
40:
21:
4161:
4160:
4156:
4155:
4154:
4152:
4151:
4150:
4116:
4115:
4114:
4109:
4091:
4047:List of numbers
4015:
4013:
4011:
4009:
3999:
3956:
3922:
3916:
3887:Graham's number
3877:Skewes's number
3779:
3777:
3775:
3769:
3764:
3734:
3729:
3693:
3674:Subtraction (1)
3669:Predecessor (0)
3657:
3638:Subtraction (1)
3633:Predecessor (0)
3618:
3572:
3570:Hyperoperations
3567:
3523:
3430:
3425:
3424:
3417:
3403:
3399:
3392:
3378:
3371:
3348:
3344:
3337:
3321:
3317:
3310:
3294:
3290:
3275:
3271:
3264:
3248:
3244:
3227:
3220:
3212:
3208:
3198:
3196:
3189:
3185:
3128:
3124:
3119:. 11 July 2014.
3111:
3110:
3106:
3091:
3087:
3082:
3077:
2953:
2944:
2921:
2917:
2910:
2904:
2895:
2890:
2873:logistic growth
2864:
2856:logistic growth
2847:
2833:
2831:Logistic growth
2793:
2790:
2789:
2782:hyperoperations
2742:
2738:
2734:
2728:
2724:
2722:
2710:
2704:
2701:
2700:
2696:
2685:
2658:
2633:
2629:
2623:
2619:
2602:
2599:
2598:
2584:
2583:
2567:
2559:
2555:
2541:
2539:
2530:
2529:
2516:
2511:
2497:
2484:
2482:
2467:
2460:
2456:
2455:
2448:
2447:
2430:
2417:
2415:
2412:
2411:
2398:
2388:
2380:
2378:
2374:
2372:
2369:
2368:
2348:
2344:
2327:
2324:
2323:
2309:
2298:
2294:
2290:
2260:
2252:
2250:
2248:
2245:
2244:
2220:
2216:
2210:
2206:
2189:
2186:
2185:
2179:
2170:
2163:
2156:
2100:
2096:
2067:
2064:
2063:
2052:
2035:
2031:
2013:
2009:
1992:
1989:
1988:
1984:
1981:
1976:
1975:
1974:
1960:
1955:
1927:
1916:
1913:
1912:
1899:
1895:
1885:
1881:
1871:
1865:
1856:
1850:
1843:
1842:corresponds to
1836:
1804:
1797:
1793:
1786:
1784:
1765:
1763:
1750:
1742:
1739:
1738:
1732:
1726:
1720:
1714:
1708:
1707:The quantities
1698:
1692:
1645:
1635:
1633:growth constant
1618:
1615:
1609:
1585:
1581:
1566:
1559:
1555:
1554:
1545:
1541:
1528:
1524:
1520:
1511:
1507:
1494:
1490:
1486:
1477:
1473:
1461:
1457:
1448:
1444:
1427:
1424:
1423:
1410:
1404:
1398:
1386:
1379:
1373:
1363:
1357:
1341:
1313:
1309:
1290:
1279:
1271:
1264:
1260:
1243:
1232:
1229:
1228:
1208:
1197:
1193:
1189:
1170:
1166:
1162:
1139:
1136:
1135:
1126:
1119:
1112:
1097:
1089:
1082:
1075:
1068:
1064:
1057:
1050:
1001:
997:
983:
979:
953:
951:
947:
918:
915:
914:
908:
904:
894:
888:
853:
850:
849:
845:
839:
818:
814:
810:
787:
784:
783:
779:
775:
758:
757:
747:
741:
740:
730:
723:
717:
716:
706:
699:
697:
694:
693:
692:
671:
670:
660:
654:
653:
643:
637:
636:
626:
619:
617:
614:
613:
612:
605:
592:social networks
575:
565:
558:
554:
550:
538:
531:
524:
520:
494:
481:Pyramid schemes
467:
457:
403:that undergoes
394:nuclear weapons
348:
310:
301:
290:
284:
281:
270:
258:
239:
228:logistic growth
210:
207:
201:
182:
178:
160:
156:
147:
143:
141:
138:
137:
131:
127:
123:
113:geometric decay
57:
53:
51:
44:
42:
38:
28:
23:
22:
15:
12:
11:
5:
4159:
4149:
4148:
4143:
4138:
4133:
4128:
4111:
4110:
4108:
4107:
4102:
4096:
4093:
4092:
4090:
4089:
4084:
4079:
4077:Power of three
4074:
4069:
4064:
4059:
4057:Number systems
4054:
4049:
4044:
4039:
4034:
4029:
4024:
4018:
4016:
4012:(alphabetical
4005:
4004:
4001:
4000:
3998:
3997:
3992:
3987:
3982:
3981:
3980:
3975:
3968:Hyperoperation
3964:
3962:
3958:
3957:
3955:
3954:
3949:
3944:
3939:
3933:
3931:
3924:
3918:
3917:
3915:
3914:
3909:
3904:
3899:
3894:
3889:
3884:
3882:Moser's number
3879:
3874:
3869:
3867:Shannon number
3864:
3859:
3854:
3849:
3844:
3839:
3834:
3829:
3824:
3819:
3814:
3809:
3804:
3799:
3794:
3789:
3783:
3781:
3771:
3770:
3763:
3762:
3755:
3748:
3740:
3731:
3730:
3728:
3727:
3722:
3717:
3712:
3707:
3701:
3699:
3695:
3694:
3692:
3691:
3686:
3681:
3676:
3671:
3665:
3663:
3659:
3658:
3656:
3655:
3653:Super-root (4)
3650:
3645:
3640:
3635:
3629:
3627:
3620:
3619:
3617:
3616:
3611:
3606:
3601:
3596:
3591:
3586:
3580:
3578:
3574:
3573:
3566:
3565:
3558:
3551:
3543:
3537:
3536:
3530:
3529:— Presentation
3522:
3521:External links
3519:
3518:
3517:
3506:
3492:
3478:
3464:
3448:
3429:
3426:
3423:
3422:
3415:
3397:
3390:
3369:
3342:
3335:
3315:
3308:
3288:
3283:YouTube Trends
3269:
3262:
3242:
3218:
3206:
3183:
3146:(3): 705–714.
3122:
3104:
3084:
3083:
3081:
3078:
3076:
3075:
3070:
3065:
3060:
3055:
3050:
3045:
3040:
3035:
3030:
3025:
3020:
3015:
3010:
3005:
3000:
2995:
2990:
2985:
2983:Bounded growth
2980:
2975:
2970:
2965:
2960:
2954:
2952:
2949:
2943:
2940:
2920:grains on the
2903:
2900:
2894:
2891:
2863:
2860:
2845:Logistic curve
2843:Main article:
2832:
2829:
2812:
2809:
2806:
2803:
2800:
2797:
2756:
2753:
2745:
2741:
2737:
2731:
2727:
2719:
2716:
2713:
2709:
2684:
2681:
2644:
2639:
2636:
2632:
2626:
2622:
2618:
2615:
2612:
2609:
2606:
2582:
2579:
2576:
2573:
2570:
2568:
2562:
2558:
2553:
2550:
2547:
2544:
2538:
2535:
2532:
2531:
2528:
2525:
2519:
2514:
2510:
2506:
2503:
2500:
2498:
2494:
2490:
2487:
2479:
2476:
2473:
2470:
2463:
2459:
2454:
2450:
2449:
2446:
2443:
2439:
2436:
2433:
2431:
2427:
2423:
2420:
2414:
2413:
2410:
2407:
2404:
2401:
2399:
2394:
2391:
2386:
2383:
2377:
2376:
2351:
2347:
2343:
2340:
2337:
2334:
2331:
2278:
2275:
2272:
2266:
2263:
2258:
2255:
2239:satisfies the
2226:
2223:
2219:
2213:
2209:
2205:
2202:
2199:
2196:
2193:
2178:
2175:
2138:
2135:
2132:
2129:
2126:
2123:
2120:
2117:
2114:
2111:
2108:
2103:
2099:
2095:
2092:
2089:
2086:
2083:
2080:
2077:
2074:
2071:
2056:grows linearly
2038:
2034:
2030:
2027:
2024:
2021:
2016:
2012:
2008:
2005:
2002:
1999:
1996:
1983:If a variable
1980:
1977:
1957:
1956:
1949:
1948:
1947:
1934:
1930:
1926:
1923:
1920:
1822:
1817:
1811:
1808:
1803:
1800:
1796:
1792:
1789:
1783:
1778:
1774:
1771:
1768:
1762:
1757:
1754:
1749:
1746:
1705:
1704:
1689:
1677:
1664:e-folding time
1659:
1613:
1597:
1592:
1588:
1584:
1579:
1573:
1570:
1565:
1562:
1558:
1553:
1548:
1544:
1540:
1535:
1531:
1527:
1523:
1519:
1514:
1510:
1506:
1501:
1497:
1493:
1489:
1485:
1480:
1476:
1472:
1467:
1464:
1460:
1456:
1451:
1447:
1443:
1440:
1437:
1434:
1431:
1324:
1321:
1316:
1312:
1308:
1305:
1302:
1297:
1289:
1286:
1282:
1278:
1270:
1267:
1263:
1259:
1256:
1253:
1250:
1242:
1239:
1236:
1215:
1207:
1204:
1200:
1196:
1192:
1188:
1185:
1182:
1177:
1173:
1169:
1165:
1161:
1158:
1155:
1152:
1149:
1146:
1143:
1036:
1032:
1029:
1026:
1023:
1020:
1017:
1014:
1008:
1005:
1000:
996:
990:
987:
982:
978:
975:
972:
966:
962:
959:
956:
950:
946:
943:
940:
937:
934:
931:
928:
925:
922:
876:
872:
869:
866:
863:
860:
857:
825:
821:
817:
813:
809:
806:
803:
800:
797:
794:
791:
756:
753:
750:
748:
746:
743:
742:
737:
734:
729:
726:
724:
722:
719:
718:
715:
712:
709:
707:
705:
702:
701:
669:
666:
663:
661:
659:
656:
655:
652:
649:
646:
644:
642:
639:
638:
635:
632:
629:
627:
625:
622:
621:
604:
601:
600:
599:
580:internet memes
574:
571:
570:
569:
513:
493:
490:
489:
488:
478:
466:
463:
462:
461:
456:
453:
452:
451:
433:
383:
347:
344:
343:
342:
327:
315:microorganisms
313:The number of
309:
306:
303:
302:
261:
259:
252:
238:
235:
205:
185:
181:
177:
174:
171:
168:
163:
159:
155:
150:
146:
68:(that is, the
66:rate of change
52:
43:
37:
26:
9:
6:
4:
3:
2:
4158:
4147:
4146:Growth curves
4144:
4142:
4139:
4137:
4134:
4132:
4129:
4127:
4124:
4123:
4121:
4106:
4103:
4101:
4098:
4097:
4094:
4088:
4085:
4083:
4080:
4078:
4075:
4073:
4070:
4068:
4065:
4063:
4060:
4058:
4055:
4053:
4050:
4048:
4045:
4043:
4040:
4038:
4037:Infinitesimal
4035:
4033:
4030:
4028:
4025:
4023:
4020:
4019:
4017:
4006:
3996:
3993:
3991:
3988:
3986:
3983:
3979:
3976:
3974:
3971:
3970:
3969:
3966:
3965:
3963:
3959:
3953:
3950:
3948:
3945:
3943:
3940:
3938:
3935:
3934:
3932:
3928:
3925:
3919:
3913:
3910:
3908:
3907:Rayo's number
3905:
3903:
3900:
3898:
3895:
3893:
3890:
3888:
3885:
3883:
3880:
3878:
3875:
3873:
3870:
3868:
3865:
3863:
3860:
3858:
3855:
3853:
3850:
3848:
3845:
3843:
3840:
3838:
3835:
3833:
3830:
3828:
3825:
3823:
3820:
3818:
3815:
3813:
3810:
3808:
3805:
3803:
3800:
3798:
3795:
3793:
3790:
3788:
3785:
3784:
3782:
3772:
3768:
3767:Large numbers
3761:
3756:
3754:
3749:
3747:
3742:
3741:
3738:
3726:
3723:
3721:
3718:
3716:
3713:
3711:
3708:
3706:
3703:
3702:
3700:
3696:
3690:
3687:
3685:
3684:Logarithm (3)
3682:
3680:
3677:
3675:
3672:
3670:
3667:
3666:
3664:
3660:
3654:
3651:
3649:
3646:
3644:
3641:
3639:
3636:
3634:
3631:
3630:
3628:
3625:
3621:
3615:
3612:
3610:
3609:Pentation (5)
3607:
3605:
3604:Tetration (4)
3602:
3600:
3597:
3595:
3592:
3590:
3587:
3585:
3584:Successor (0)
3582:
3581:
3579:
3575:
3571:
3564:
3559:
3557:
3552:
3550:
3545:
3544:
3541:
3534:
3531:
3528:
3525:
3524:
3515:
3511:
3507:
3505:
3504:0-471-74747-5
3501:
3497:
3493:
3491:
3490:0-415-42060-1
3487:
3483:
3479:
3477:
3476:1-84407-192-8
3473:
3469:
3465:
3463:
3462:0-87663-165-0
3459:
3455:
3454:
3449:
3447:
3446:9781603581554
3443:
3439:
3437:
3432:
3431:
3418:
3416:9781603581554
3412:
3408:
3401:
3393:
3391:1-84407-192-8
3387:
3383:
3376:
3374:
3365:
3361:
3357:
3353:
3346:
3338:
3332:
3328:
3327:
3319:
3311:
3305:
3301:
3300:
3292:
3284:
3280:
3273:
3265:
3259:
3255:
3254:
3246:
3237:
3232:
3225:
3223:
3215:
3210:
3194:
3187:
3179:
3175:
3170:
3165:
3161:
3157:
3153:
3149:
3145:
3141:
3137:
3133:
3126:
3118:
3117:HowStuffWorks
3114:
3108:
3100:
3096:
3089:
3085:
3074:
3071:
3069:
3066:
3064:
3061:
3059:
3058:Menger sponge
3056:
3054:
3051:
3049:
3046:
3044:
3041:
3039:
3036:
3034:
3031:
3029:
3026:
3024:
3021:
3019:
3016:
3014:
3011:
3009:
3006:
3004:
3001:
2999:
2996:
2994:
2991:
2989:
2986:
2984:
2981:
2979:
2976:
2974:
2971:
2969:
2966:
2964:
2961:
2959:
2956:
2955:
2948:
2939:
2937:
2932:
2930:
2915:
2909:
2899:
2889:
2885:
2881:
2876:
2874:
2870:
2859:
2857:
2853:
2846:
2837:
2828:
2826:
2807:
2804:
2801:
2795:
2787:
2784:beginning at
2783:
2779:
2774:
2772:
2767:
2754:
2751:
2743:
2739:
2735:
2729:
2725:
2711:
2694:
2690:
2680:
2678:
2674:
2669:
2667:
2661:
2655:
2642:
2637:
2634:
2630:
2624:
2620:
2616:
2610:
2604:
2580:
2577:
2574:
2571:
2569:
2560:
2556:
2548:
2542:
2536:
2533:
2526:
2523:
2517:
2512:
2508:
2504:
2501:
2499:
2492:
2488:
2485:
2474:
2468:
2461:
2457:
2452:
2444:
2441:
2437:
2434:
2432:
2425:
2421:
2418:
2408:
2405:
2402:
2400:
2392:
2389:
2384:
2381:
2365:
2349:
2345:
2341:
2335:
2329:
2322:
2321:initial value
2316:
2312:
2305:
2301:
2276:
2273:
2270:
2264:
2261:
2256:
2253:
2242:
2224:
2221:
2217:
2211:
2207:
2203:
2197:
2191:
2184:
2174:
2167:
2162:
2154:
2149:
2136:
2130:
2127:
2124:
2118:
2115:
2112:
2109:
2106:
2101:
2097:
2093:
2090:
2087:
2081:
2075:
2072:
2069:
2061:
2057:
2036:
2028:
2025:
2022:
2014:
2010:
2006:
2000:
1994:
1972:
1968:
1964:
1959:
1953:
1946:
1932:
1928:
1924:
1921:
1918:
1910:
1905:
1902:
1892:
1888:
1878:
1874:
1868:
1862:
1859:
1853:
1846:
1839:
1820:
1815:
1809:
1806:
1801:
1798:
1794:
1790:
1787:
1781:
1776:
1772:
1769:
1766:
1760:
1755:
1752:
1747:
1744:
1735:
1729:
1723:
1717:
1711:
1701:
1695:
1690:
1687:
1684:
1683:
1682:doubling time
1678:
1675:
1674:
1669:
1666:
1665:
1660:
1657:
1653:
1648:
1643:
1638:
1634:
1630:
1629:
1628:
1625:
1621:
1612:
1595:
1590:
1586:
1582:
1577:
1571:
1568:
1563:
1560:
1556:
1551:
1546:
1542:
1538:
1533:
1529:
1525:
1521:
1517:
1512:
1508:
1504:
1499:
1495:
1491:
1487:
1483:
1478:
1474:
1470:
1465:
1462:
1458:
1454:
1449:
1445:
1441:
1435:
1429:
1421:
1416:
1413:
1407:
1401:
1396:
1395:
1389:
1383:
1376:
1371:
1366:
1360:
1355:
1354:dimensionless
1349:
1345:
1338:
1335:
1322:
1319:
1314:
1310:
1306:
1303:
1300:
1287:
1280:
1268:
1261:
1257:
1254:
1251:
1240:
1234:
1205:
1198:
1194:
1190:
1186:
1183:
1180:
1175:
1171:
1167:
1163:
1159:
1156:
1153:
1147:
1141:
1133:
1129:
1122:
1115:
1110:
1105:
1103:
1093:
1085:
1078:
1071:
1060:
1053:
1047:
1034:
1030:
1027:
1021:
1015:
1012:
1006:
1003:
998:
994:
988:
985:
980:
976:
973:
970:
964:
960:
957:
954:
948:
944:
941:
938:
932:
929:
926:
920:
911:
902:
901:time constant
897:
891:
887:the constant
874:
870:
867:
861:
855:
842:
823:
819:
815:
811:
807:
804:
801:
795:
789:
754:
751:
749:
744:
735:
732:
727:
725:
720:
713:
710:
708:
703:
689:
667:
664:
662:
657:
650:
647:
645:
640:
633:
630:
628:
623:
609:
603:Basic formula
597:
596:Gangnam Style
593:
589:
585:
581:
577:
576:
561:
548:
541:
534:
527:
518:
514:
511:
507:
503:
499:
496:
495:
486:
485:Ponzi schemes
482:
479:
476:
472:
469:
468:
459:
458:
449:
445:
441:
440:amplification
437:
434:
430:
426:
422:
418:
414:
410:
406:
402:
399:
395:
391:
387:
384:
381:
377:
373:
369:
365:
361:
357:
353:
350:
349:
340:
336:
332:
328:
324:
320:
316:
312:
311:
299:
296:
288:
278:
274:
268:
267:
262:This section
260:
256:
251:
250:
243:
234:
231:
229:
225:
221:
216:
204:
198:
183:
175:
172:
169:
161:
157:
153:
148:
144:
135:
120:
118:
114:
110:
106:
102:
97:
95:
91:
87:
83:
79:
75:
71:
67:
63:
50:
34:
30:
19:
4131:Exponentials
4072:Power of two
4062:Number names
3797:Ten thousand
3679:Division (2)
3643:Division (2)
3614:Hexation (6)
3589:Addition (1)
3513:
3495:
3481:
3467:
3466:Porritt, J.
3451:
3434:
3406:
3400:
3381:
3355:
3351:
3345:
3325:
3318:
3298:
3291:
3282:
3272:
3252:
3245:
3209:
3197:. Retrieved
3186:
3143:
3140:Cell Reports
3139:
3125:
3116:
3107:
3098:
3088:
2968:Arthrobacter
2945:
2933:
2911:
2896:
2865:
2848:
2775:
2768:
2686:
2670:
2659:
2656:
2366:
2314:
2310:
2303:
2299:
2180:
2165:
2150:
1982:
1966:
1962:
1906:
1900:
1890:
1886:
1876:
1872:
1866:
1863:
1857:
1851:
1844:
1837:
1733:
1727:
1721:
1715:
1709:
1706:
1699:
1693:
1685:
1680:
1671:
1667:
1662:
1646:
1636:
1632:
1626:
1619:
1610:
1417:
1411:
1405:
1399:
1392:
1387:
1381:
1374:
1364:
1358:
1347:
1343:
1339:
1336:
1134:
1127:
1120:
1113:
1108:
1106:
1091:
1083:
1076:
1069:
1058:
1051:
1048:
909:
895:
889:
840:
773:
559:
539:
532:
525:
510:Ray Kurzweil
375:
339:immunization
291:
282:
271:Please help
266:verification
263:
232:
224:viral videos
202:
199:
136:
121:
112:
108:
98:
74:proportional
61:
60:
49:Cubic growth
29:
4082:Power of 10
4022:Busy beaver
3827:Quintillion
3822:Quadrillion
3253:Going Viral
3073:Stein's law
3063:Moore's law
2988:Cell growth
1971:SVG version
1911:, that is,
1340:Many pairs
774:A quantity
547:Moore's Law
502:Moore's law
417:probability
285:August 2013
90:the inverse
4120:Categories
4087:Sagan Unit
3921:Expression
3872:Googolplex
3837:Septillion
3832:Sextillion
3778:numerical
3080:References
2942:Water lily
2914:chessboard
2906:See also:
2693:polynomial
2159:, one can
2060:logarithms
1909:rule of 70
562:+ constant
475:rule of 72
356:dielectric
130:, as time
70:derivative
3978:Pentation
3973:Tetration
3961:Operators
3930:Notations
3852:Decillion
3847:Nonillion
3842:Octillion
3774:Examples
3236:1402.3499
3160:2211-1247
3053:Power law
2786:tetration
2730:α
2718:∞
2715:→
2673:nonlinear
2537:
2509:∫
2453:∫
2119:
2113:⋅
2094:
2073:
1922:≃
1791:
1770:
1756:τ
1642:frequency
1552:⋅
1518:⋅
1500:τ
1484:⋅
1455:⋅
1307:⋅
1292: min
1273: min
1258:⋅
1210: min
1187:⋅
1176:τ
1160:⋅
1107:Example:
1028:⋅
1007:τ
1004:τ
995:⋅
989:τ
977:⋅
965:τ
961:τ
945:⋅
933:τ
824:τ
808:⋅
455:Economics
444:resonance
376:secondary
372:molecules
354:within a
4010:articles
4008:Related
3912:Infinity
3817:Trillion
3792:Thousand
3178:24767987
3003:EXPSPACE
2951:See also
2929:trillion
2597:so that
2319:has the
2293:at time
1245: hr
1130:= 10 min
588:go viral
553:in time
421:function
413:absorbed
409:neutrons
396:). Each
360:electron
335:smallpox
331:COVID-19
237:Examples
78:function
4105:History
3923:methods
3897:SSCG(3)
3892:TREE(3)
3812:Billion
3807:Million
3787:Hundred
3624:Inverse
3577:Primary
3428:Sources
3169:4049626
3008:EXPTIME
1965:and 72/
1849:and to
1640:is the
1096:, then
1090:0 <
1063:, then
899:is the
465:Finance
423:of the
405:fission
401:nucleus
398:uranium
346:Physics
319:culture
308:Biology
4014:order)
3862:Googol
3502:
3488:
3474:
3460:
3444:
3413:
3388:
3333:
3306:
3260:
3199:26 May
3176:
3166:
3158:
2926:a.k.a.
2886:, and
2788:, and
2671:For a
2662:< 0
2308:, and
1835:where
1719:, and
1608:where
1094:< 1
1086:> 0
1079:> 1
1072:< 0
1061:> 1
1054:> 0
584:videos
323:splits
215:colony
200:where
105:domain
54:
47:
45:
39:
4100:Names
3902:BH(3)
3780:order
3231:arXiv
2934:The "
1731:also
1654:, or
1352:of a
1081:, or
425:shape
368:atoms
333:, or
317:in a
3500:ISBN
3486:ISBN
3472:ISBN
3458:ISBN
3442:ISBN
3411:ISBN
3386:ISBN
3331:ISBN
3304:ISBN
3258:ISBN
3201:2009
3174:PMID
3156:ISSN
2181:The
2164:log
1855:and
1679:The
1661:The
1631:The
1420:base
1380:log
1125:and
1100:has
1088:and
1074:and
1056:and
542:= 12
535:= 11
528:= 10
504:and
429:mass
427:and
392:and
3360:doi
3164:PMC
3148:doi
2858:".
2708:lim
2169:on
2116:log
2091:log
2070:log
1864:If
1847:= 0
1840:= 0
1810:100
1622:(0)
1572:100
1368:(a
1323:64.
1123:= 2
1116:= 1
1049:If
782:if
582:or
515:In
483:or
370:or
275:by
111:or
92:of
4122::
3776:in
3512:.
3372:^
3356:64
3354:.
3281:.
3221:^
3172:.
3162:.
3154:.
3142:.
3138:.
3115:.
3097:.
2882:,
2827:.
2773:.
2755:0.
2699::
2679:.
2668:.
2534:ln
2364:.
2243::
2173:.
1945:.
1925:70
1788:ln
1767:ln
1713:,
1624:.
1415:.
1346:,
1288:10
1269:60
1206:10
1132:.
1118:,
1104:.
913::
848:,
714:24
512:.)
230:.
119:.
96:.
3759:e
3752:t
3745:v
3562:e
3555:t
3548:v
3419:.
3394:.
3366:.
3362::
3339:.
3312:.
3285:.
3266:.
3239:.
3233::
3203:.
3180:.
3150::
3144:7
3101:.
2922:n
2918:2
2811:)
2808:n
2805:,
2802:n
2799:(
2796:A
2752:=
2744:t
2740:e
2736:a
2726:t
2712:t
2697:α
2660:k
2643:.
2638:t
2635:k
2631:e
2625:0
2621:x
2617:=
2614:)
2611:t
2608:(
2605:x
2581:.
2578:t
2575:k
2572:=
2561:0
2557:x
2552:)
2549:t
2546:(
2543:x
2527:t
2524:d
2518:t
2513:0
2505:k
2502:=
2493:x
2489:x
2486:d
2478:)
2475:t
2472:(
2469:x
2462:0
2458:x
2445:t
2442:d
2438:k
2435:=
2426:x
2422:x
2419:d
2409:x
2406:k
2403:=
2393:t
2390:d
2385:x
2382:d
2350:0
2346:x
2342:=
2339:)
2336:0
2333:(
2330:x
2317:)
2315:t
2313:(
2311:x
2306:)
2304:t
2302:(
2300:x
2295:t
2291:x
2277:x
2274:k
2271:=
2265:t
2262:d
2257:x
2254:d
2225:t
2222:k
2218:e
2212:0
2208:x
2204:=
2201:)
2198:t
2195:(
2192:x
2171:t
2166:x
2157:x
2137:.
2134:)
2131:r
2128:+
2125:1
2122:(
2110:t
2107:+
2102:0
2098:x
2088:=
2085:)
2082:t
2079:(
2076:x
2053:x
2037:t
2033:)
2029:r
2026:+
2023:1
2020:(
2015:0
2011:x
2007:=
2004:)
2001:t
1998:(
1995:x
1985:x
1967:t
1963:t
1933:r
1929:/
1919:T
1901:p
1896:t
1891:p
1889:/
1887:t
1882:t
1877:p
1875:/
1873:t
1867:p
1858:T
1852:τ
1845:r
1838:k
1821:p
1816:)
1807:r
1802:+
1799:1
1795:(
1782:=
1777:T
1773:2
1761:=
1753:1
1748:=
1745:k
1734:r
1728:p
1722:T
1716:τ
1710:k
1703:.
1700:p
1694:r
1686:T
1676:.
1673:e
1668:τ
1658:.
1647:e
1637:k
1620:x
1614:0
1611:x
1596:,
1591:p
1587:/
1583:t
1578:)
1569:r
1564:+
1561:1
1557:(
1547:0
1543:x
1539:=
1534:T
1530:/
1526:t
1522:2
1513:0
1509:x
1505:=
1496:/
1492:t
1488:e
1479:0
1475:x
1471:=
1466:t
1463:k
1459:e
1450:0
1446:x
1442:=
1439:)
1436:t
1433:(
1430:x
1412:b
1406:τ
1400:τ
1394:e
1388:b
1382:b
1375:τ
1365:τ
1359:b
1350:)
1348:τ
1344:b
1342:(
1320:=
1315:6
1311:2
1304:1
1301:=
1296:)
1285:(
1281:/
1277:)
1266:(
1262:2
1255:1
1252:=
1249:)
1241:1
1238:(
1235:x
1214:)
1203:(
1199:/
1195:t
1191:2
1184:1
1181:=
1172:/
1168:t
1164:b
1157:a
1154:=
1151:)
1148:t
1145:(
1142:x
1128:τ
1121:b
1114:a
1098:x
1092:b
1084:τ
1077:b
1070:τ
1065:x
1059:b
1052:τ
1035:.
1031:b
1025:)
1022:t
1019:(
1016:x
1013:=
999:b
986:t
981:b
974:a
971:=
958:+
955:t
949:b
942:a
939:=
936:)
930:+
927:t
924:(
921:x
910:b
905:x
896:τ
890:b
875:,
871:a
868:=
865:)
862:0
859:(
856:x
846:x
841:a
820:/
816:t
812:b
805:a
802:=
799:)
796:t
793:(
790:x
780:t
776:x
755:5
752:=
745:r
736:2
733:1
728:=
721:b
711:=
704:a
668:5
665:=
658:r
651:2
648:=
641:b
634:3
631:=
624:a
566:t
560:x
555:t
551:x
540:x
533:x
526:x
521:2
477:.
298:)
292:(
287:)
283:(
269:.
211:x
206:0
203:x
184:t
180:)
176:r
173:+
170:1
167:(
162:0
158:x
154:=
149:t
145:x
132:t
128:r
124:x
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
