exponentially

From exponential +‎ -ly.

• (UK) IPA^(key): /ɛkspə(ʊ)ˈnɛnʃəli/

exponentially (comparative more exponentially, superlative most exponentially)

1. (mathematics, sciences) In an exponential manner.
   • 1992, Clark Glymour, Thinking Things Through: An Introduction to Philosophical Issues and Achievements, MIT Press (1997), →ISBN, page 333:

     But every known algorithm for this problem requires a number of steps that increases exponentially as n increases.

   • 2000, Shuji Nakamura et al., The Blue Laser Diode: The Complete Story, Second Revised and Enlarged Edition, Springer, →ISBN, page 69:

     Therefore, if absorption causes an attenuation of the oscillation amplitude, the temperature must decrease exponentially with increasing thickness.

   • 2008, Henri Benisty et al., Photonic Crystals: Towards Nanoscale Photonic Devices, Second Edition, Springer, →ISBN, page 216:

     It can be readily derived from Eqs. 6.26 and 6.32 that the field generated by these incident evanescent waves inside the slab do ^[sic] not decay away exponentially from the upper interface, but increases exponentially as y decreases.

2. (proscribed) rapidly, greatly
   • 2007, Michael Glenn Maness, Would You Lie to Save a Life: Love Will Find a Way Home, page 357:

     The more serious a Christian is about God's kingdom, the more exponentially complicating that venture is […]

   • 2008, Beth Kery, Take a Stranger No More, page 27:

     He'd felt like Kathryn's soul was in her eyes as she'd regarded him for those precious few seconds... and her spirit was even more exponentially beautiful than […]