exponentialadj.n.
/ˌɛkspə(ʊ)ˈnɛnʃl/, U.S. /ˌɛkspəˈnɛn(t)ʃ(ə)l/ A. adj.
1.
a. Mathematics. Of an equation or quantity: involving a variable as (part of) an exponent (exponent n. 2a). Also: represented by or relating to such an equation or quantity; esp. (of a process or phenomenon) proceeding with something multiplied by a constant factor in successive equal periods of time (cf. exponential decay n., exponential growth n. at Compounds).Earliest in exponential equation n. at Compounds.
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the world > relative properties > number > algebra > [adjective] > relating to expressions > relating to functions
generating1671
exponential1704
discontinuous1803
functional1806
odd1812
periodic1820
syzygetic1850
convex1858
graphometric1865
polycyclic1869
subrational1875
synectic1876
variational1879
polyhedral1881
holomorphic1886
tropical1887
Gudermannian1888
monogeneous1888
monotonous1890
oscillating1893
monotonic1901
monotone1903
orthogonalized1909
schlicht1925
concave1942
deconvolved1974
unate1978
1701 G. Cheyne New Theory Acute & Slow Continu'd Fevers (ed. 2) 30 I know of something like the same done for all Curves and Solids, whose natures are express'd by Transcendent or Exponential Æquations.
1784 Philos. Trans. (Royal Soc.) 74 401 P is either an algebraical, exponential, or fluential fluxion of X.
1796 C. Hutton Math. & Philos. Dict. Exponential Calculus the method of differencing or finding the fluxions of Exponential quantities, and of summing up those differences or finding their fluents.
1881 J. C. Maxwell Treat. Electr. & Magnetism (ed. 2) I. 221 We call the exponential quantity..the hyperbolic cosine of β.
1954 E. P. Abraham in H. W. Florey Lect. Gen. Pathol. xiii. 246 Hence the survival curve is exponential and a straight line is obtained on plotting the dose against the logarithm of the surviving fraction.
1971 Amer. Naturalist 105 137 Population growth is exponential in our first model and logistic in the second, more realistic one.
2018 J. MacCormick What can be computed? xvi. 295 The width of a given layer of the tree could be exponential, because the number of threads can grow by a constant factor at each layer.
b. Of an increase or change: becoming more and more rapid; (of the rate or effect of an increase or change) becoming greater and greater; ever increasing. Also more generally: very rapid; very great.
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the world > relative properties > quantity > greatness of quantity, amount, or degree > [adjective] > very great
swappingc1440
bumping1566
thumping1576
swingeinga1592
knocking1598
gigantical1604
gigantine1605
gigantean1611
gigantal?1614
thundering1618
whoppinga1625
humming1654
rapping1657
whisking1673
threshing1707
sousing1735
nation1765
heroic1785
runaway1790
spanking1791
gigantic1797
whacking1797
cracking1834
ringing1834
bouncing1842
walloping1847
stavingc1850
banging1864
howling1865
whooping1866
smacking1888
God almighty1913
Christ almighty1961
the world > relative properties > quantity > increase in quantity, amount, or degree > [adjective] > increasing continuously
accrescent1713
accretive1796
the world > relative properties > quantity > increase in quantity, amount, or degree > [adjective] > increasing rapidly or sharply
fast-growing1597
skyrocketing1833
skyrockety1856
bounding1887
ballooning1896
mushrooming1954
rocketing1959
1955 Washington Post 26 June e1/5 Beginning then, progress moved at an exponential rate.
1989 Toronto Star (Nexis) 9 May (Final ed.) a20 Stricter sentencing and an exponential increase in drug arrests are turning the United States into a nation of prisoners and guards.
1997 Observer 20 July 18/4 The Eurostar travels at exponential speeds through France but slows to a crawl in Kent.
2006 Independent 13 Oct. 21/2 Fairly traded food goods have seen exponential growth over the past five years, with a 265 per cent increase in sales.
2. That serves to describe or display; expository. rare.
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the mind > language > statement > [adjective]
enunciative1531
exponent1581
definitivea1620
pronouncing1628
declarative1642
declaratory1660
enunciatory1693
exponential1730
statemental1880
1730 N. Bailey et al. Dictionarium Britannicum Exponential,..expounding, laying open to view.
1818 S. T. Coleridge Friend (new ed.) III. 185 Where the hypothesis is an exponential image..of an idea.
1901 Inquirer & Commerc. News (Perth, Austral.) 29 Mar. 2/6 With the advancement of many of her pupils..the Muses have instructed her in the art, both exponential and practical.
2000 T. Moylan Scraps of Unpainted Sky p. xiii The mise-en-scène is established in an exponential presentation of the society's structure and operation.
B. n.
Mathematics. An expression consisting of a number with an exponent (exponent n. 2a); a quantity represented by or relating to such expressions; spec. the function ez, where e is Euler's number (E n.1 7a) and z is a real or complex variable.If z is a complex variable, x + iy, then ez = ex(cos(y) + isin(y)) and so involves trigonometric functions.
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the world > relative properties > number > algebra > [noun] > expression > function
function1758
exponential1784
potential function1828
syzygy1850
permutant1852
Green function1863
theta-function1871
Greenian1876
Gudermannian1876
discriminoid1877
Weierstrassian function1878
gradient1887
beta function1888
distribution function1889
Riemann zeta function1899
Airy integral1903
Poisson bracket1904
Stirling approximation1908
functional1915
metric1921
Fourier transform1923
recursive function1934
utility function1934
Airy function1939
transfer function1948
objective function1949
restriction1949
multifunction1954
restriction mapping1956
scalar function1956
Langevin function1960
mass function1961
1704 C. Hayes Treat. Fluxions xv. 310 An Equation consists of several Exponentials of different Degrees.
1784 E. Waring in Philos. Trans. (Royal Soc.) 74 395 When the terms are exponentials of superior orders.
1833 Sir W. R. Hamilton Let. 15 Oct. in R. P. Graves Life Sir W. R. Hamilton (1885) II. 58 My extension of Herschel's theorem for the development of functions of exponentials.
1901 Horseless Age 13 Nov. 714/1 The compression and expansion curves on the p. v. diagram are exponentials and theoretically both have the same exponent.
1918 Jrnl. Amer. Chem. Soc. 40 1866 The other exponential is essentially the cooling rate of the calorimeter.
2011 R. Kautz Chaos x. 154 The logarithm is the inverse of the exponential, and undoes whatever the exponential does.
Compounds
exponential curve n. Mathematics a curve that is the graph of an equation that includes an exponential whose exponent contains the variable, esp. one with an equation of the form y = abx, where a and b are constants. [After post-classical Latin curva exponentialis (1697); compare French courbe exponentielle (1704 or earlier).]
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1704 J. Harris Lexicon Technicum I. (at cited word) Exponential curves are such as partake both of the nature of Algebraick and Transcendent ones.
1854 Philos. Trans. (Royal Soc.) 144 69 In this form the similarity of the equations of the exponential curve and the circle is evident.
2011 J. Stewart et al. College Algebra: Concepts & Contexts iii. 295 For the third plot, it seems that an exponential curve might fit better than a line.
exponential decay n. (in mathematical modelling) decay whose rate falls in proportion to the diminishing total number or size.
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1906 E. Rutherford Radioactive Transformations iv. 102 The final exponential decay with a 28 minute period shows that another product, having a 28 minute period, is also present.
2015 J. Lehmann et al. in J. Lehmann & S. Joseph Biochar for Environmental Managem. xi. 185 Mineralization of soil organic carbon (SOC) to CO2 is commonly modelled by assuming an exponential decay.
exponential equation n. Mathematics an equation that includes an exponential whose exponent contains an unknown quantity. [After post-classical Latin aequatio exponentialis (1697).]
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1701 G. Cheyne Ess. Improvem. Theory Med. in New Theory Continu'd Fevers (ed. 2) 30 I know of something like the same done for all Curves and Solids, whose natures are express'd by Transcendent or Exponential Æquations.
1739 G. Anderson Let. in S. P. Rigaud & S. J. Rigaud Corr. Sci. Men 17th Cent. (1841) (modernized text) I. 342 The exponential equation xx = d.
1880 J. B. Thomson & E. T. Quimby Collegiate Algebra xxi. 279 An Exponential Equation is an equation in which one or more of the exponents contains an unknown quantity.
2014 L. J. Bracken & E. S. Miller Intermediate Algebra viii. 755 We can find the doubling time by solving an exponential equation.
exponential function n. Mathematics any function having a variable in an exponent; spec. the function ez where e is Euler's number (E n.1 7a) and z is a real or complex variable.
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1800 Monthly Rev. 32 App. 487 The present chapter is a rich and well-arranged repository of these methods; by which may be integrated rational functions..or irrational functions..or logarithmic and exponential functions.
1920 A. S. Gale & C. W. Watkeys Elem. Functions & Applic. v. 215 Exponential functions are important because in many fields especially in physics one variable changes increases or decreases in geometrical progression as another, frequently time, changes in arithmetical progression.
2014 C. W. Cryer Math Primer Engineers iii. 37 The exponential function is often used and it is sometimes convenient to write exp(x) instead of ex.
exponential growth n. (in mathematical modelling) growth whose rate becomes ever more rapid in proportion to the growing total number or size.
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1934 Ann. Bot. 48 938 The logarithms of the mean spike-length fell on the same straight line for each series. Thus a length and differentiation fit for flowering had been attained by slow exponential growth over a long period of time.
1949 Jrnl. Biol. Chem. 177 609 The K-12 strain grown on glucose and subcultured to fresh glucose-containing media started exponential growth with a mass doubling time of about 90 minutes.
2008 S. Boslaugh & L.-A. McNutt Encycl. Epidemiol. I. 283/2 If Q(t) has an exponential growth, then the doubling time can be exactly calculated from the constant growth rate.
exponential horn n. a horn (horn n. 15) whose cross-sectional area increases exponentially towards its open end, used to emit or receive either sound or radio waves efficiently.
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1923 Electric Jrnl. Nov. 397/2 The long exponential horn with small throat and reasonably large mouth gives about the same average response over the frequency range as does the shorter horn.
1945 Radio Craft (Springfield, Mass.) Oct. 22/1 If a highly directional beam is to be broadcast or received using the horn type antenna, an exponential horn may be used.
2013 E. J. Johnson Why you hear what you Hear xvi. 323 If we wanted to get the sound directly out of a trumpet with little reflection, we'd use an exponential horn with a wide mouth, not a trumpet—shaped one with a small mouth.
exponential-horned adj. characterized by or possessing an exponential horn (exponential horn n.).
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1954 K. Amis Lucky Jim viii. 87 The rondo of some boring piano concerto Welch had once insisted on playing him on his complicated exponential-horned gramophone.
1998 Hillandale News (London Phonogr. & Gramophone Soc.) Summer 119 (advt.) My particular wants are always: HMV cabinets; I particularly want the later exponential horned table and floor machines.
exponential pile n. Nuclear Physics (now chiefly historical) an assembly of fissionable and moderating materials, which is given an independent source of neutrons and used for experimental work, although too small to sustain a chain reaction; = exponential reactor n.So named because the neutron density was found to vary exponentially through the assembly: see quot. 1945.
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1944 T. Arnette et al. Preliminary Rep. Exponential Exper. Water-metal Rod Lattices (U.S. Atomic Energy Comm.) 6 Table I summarizes the results of the exponential pile covered in our report.
1945 H. D. Smyth Gen. Acct. Devel. Atomic Energy Mil. Purposes vi. 58 By this time [sc. 1942] it was known that the neutron density decreased exponentially with increasing distance from the neutron source (hence the name often used for experiments of this type, ‘exponential pile’).
2009 J. P. Delgado Nucl. Dawn ii. 36 The exponential piles allowed Fermi and his team to increase, slowly and a step at a time, the size of the pile.
exponential reactor n. Nuclear Physics (now chiefly historical) an assembly of fissionable and moderating materials, which is given an independent source of neutrons and used for experimental work, although too small to sustain a chain reaction; = exponential pile n.
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1951 A. H. Barnes et al. Exponential Exper. Argonne National Lab. 39/1 An exponential reactor may be formally defined as a small reactor constructed so that leakage prevents a chain reaction even if the reproduction factor K is greater than 1.
2017 D. N. Schwartz Last Man who knew Everything xvii. 206 Fermi calculated that the internal uranium lattice would result in a fully operational exponential reactor when the pile rose to seventy-six layers, just below twenty-seven feet high.
exponential series n. Mathematics an infinite series having the form 1 + z + z2/2! + z3/3! … + zn/n! + …, which converges to the exponential function ez.
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1814 P. Barlow New Math. Tables 277 (heading) Exponential series.
1940 W. J. Eckert Punched Card Methods Sci. Computation vii. 66 Exponential series are usually used for the computation of functions where both the function and its conjugate are required.
2011 D. Röss Learning & teaching Math. using Simulations iv. 46 This shows how strongly the exponential series itself converges.
exponential theorem n. Mathematics (now chiefly historical) the theorem that the infinite series having the form 1 + z + z2/2! + z3/3! … + zn/n! + …, converges to the exponential function ez.
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1826 T. Jephson Fluxional Calculus I. i. 15 (heading) The Exponential Theorem.
1907 E. W. Hobson Theory of Functions of Real Variable vi. 494 In order to extend the proof of the exponential theorem to the case of an irrational value of x, we observe that the above series converges uniformly.
1994 M. A. McBeth Combinatorial Number Theory ii. 89 The classical theory is founded on the exponential theorem.
exponential time n. Computing an amount of time (for the completion of an algorithm) which as a function of the amount of input data increases more rapidly than any given polynomial and which is expressed as an exponential; cf. polynomial time n.
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the world > relative properties > number > mathematics > [noun] > mathematical enquiry > proposition > problem > relating to size of
exponential time1972
1968 Math. Syst. Theory 2 278 A one-way CM [= Counter Machine] may require exponential time to simulate a real-time one-tape TM [= Turing Machine].
1985 P. W. Purdom & C. A. Brown Anal. Algorithms i. 3 Exponential time algorithms (such as those that use time 2n or en) are suitable only for small problems, even when the fastest computers are used.
2013 S. S. Wagstaff Joy Factoring ii. 14 Some algorithms run in exponential time, which means that there is a constant C >1 so that the time the algorithm takes when the input has length l is at least Cl time units.
This entry has been updated (OED Third Edition, September 2022).
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adj.n.1701