# Word or phrase for non-linear-but-still-greater-than-linear?

I am looking to replace "exponential" in the following sentence:

"The development of new technology in this field tends to follow an (exponential) trend."

In mathematics, there are many functions which are not exponential but still increase faster than linear functions. What would be a good word/phrase to represent a trend that is growing faster than a linear function and is still open to the possibility of increasing faster or slower than an exponential function?

The first word that comes to mind is non-linear, but this term also leaves open the possibility that the trend is increasing slower than a linear function, and I would like to avoid this ambiguity.

• super-linear = faster than linear; sub-linear = slower than linear Commented Mar 31, 2016 at 14:07
• Note that below certain values, exponential, quadratic, cubic, quartic, etc. functions are increasing more slowly than linear functions. Logarithmicly increasing functions start off growing at a faster rate than linear, but then beyond certain values are growing more slowly (and never catch up after that). Note the top image here: en.wikipedia.org/wiki/Exponential_growth Commented Mar 31, 2016 at 16:14
• For technical terms, see this table of time complexities. Commented Mar 31, 2016 at 16:20
• @NickT The time complexities terms are informative and possibly helpful for people looking for other terms, but it should be noted that the term "time complexity" and the related terms are specific jargon in the field of computer science. There is a general scientific/mathematical equivalent with similar notation: en.wikipedia.org/wiki/Big_O_notation Commented Mar 31, 2016 at 16:22
• @GEdgar super-linear is exactly what I thought after reading the question and before reading the comments and answers. If this were an answer, I'd upvote. Commented Mar 31, 2016 at 17:45

The term for what you're asking is superlinear, although it may not be understood depending on your audience.

From Wiktionary:

Adjective superlinear ‎(comparative more superlinear, superlative most superlinear)

1. Above a line
2. (mathematics) Describing a function that eventually grows faster than any linear one

Merriam Webster redirects superlinear to supralinear. Unfortunately, the full definition of this word is only available in the unabridged version of MW, which is not free.

But, I did find a definition of supralinear at Wiktionary:

1. (typography) above the lines of normal text
2. (mathematics) greater than linear

You might be better off phrasing things a different way, like saying that the growth rate is 'accelerating', or using "more and more" or something similar.

Perhaps you could say that "development of new technology in this field is accelerating".

In my view, "accelerating development" would mean that there was more development in 2015 that there was in 2010.

You are probably looking for polynomial. Linear functions are polynomial, but are the slowest growing polynomials. All polynomials (eventually) grow more slowly than exponentials.

• Polynomial functions may be decreasing. Commented Mar 31, 2016 at 15:11
• @EdwinAshworth Linear and exponential functions may be decreasing. It's important when using a terms that discusses the rate of increase or decrease (like "linear", "polynomial", or "exponential") that there be another term indicating increase or decrease, such as "exponential growth" or "increases linearly over time". Commented Mar 31, 2016 at 16:08
• There are more specific ways to indicate "polynomial" growth or decay that are more commonly used, such as "quadratic" or "cubic", which also clarifies that the growth or decay is steeper than linear, since linear functions are also polynomials. Commented Mar 31, 2016 at 16:11
• @Todd Wilcox The Gricean Maxim of quantity means that 'All polynomials (eventually) grow more slowly ...' entails 'All polynomials (eventually) grow '. But another problem with this answer is that 'polynomially' ('quadratically ...'haven't the extended usage that 'exponentially' (meaning just 'very and increasingly rapidly') has. Commented Mar 31, 2016 at 16:13
• The asker said that the term needs to include the possibility of being exponential, which polynomial does not. Commented Mar 31, 2016 at 19:56

You could use Geometric growth. It fits in between the linear and exponential curves, and is a term that may be understood outside of mathematics or computer science.