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I'm speaking about a particular quantity, let us call it the number of gizmos, which depends on the number of thingums, doodahs, and hickeys. Mathematically, we have a function g which is represented by an expression with variables t, d, and h.

Now, I want to roughly say that g(t,d,h) ≤ , where a and b are some expressions exceeding 1 and depending on t and d, but not on h.

Intentionally simplifying, I wrote:

The number of gizmos is exponential in the number of hickeys.

In this style, I used to write for over a decade. But my English teacher corrected the sentence to

The number of gizmos grows exponentially in terms of the number of hickeys.

I can live with "grows" but find "terms of" strange. Which version is right? If both, which style is preferred in math papers?

I welcome answers from mathematicians who are native AmE speakers and have an excellent command of English.

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I am a native speaker and teach mathematics for a living. "In" is simply not correct here. As @FumbleFingers indicated in his comment, the standard usage here would "grows exponentially with" or "rises exponentially with". Grows or rises are both fine synonyms in this instance.

"In terms of" is a grammatically legal construction, but it isn't quite right, either. "In terms of" when used to describe a mathematical function is typically synonymous with "as measured by". You can see that usage in this gem from the Journal of Infometrics: "International collaboration as measured by co-authorship relations on refereed papers grew linearly from 1990 to 2005 in terms of the number of papers, but exponentially in terms of the number of international addresses."

  • I am also a native speaker with degrees in mathematics and engineering, and I agree that "grows..with" is the standard way of saying this. books.google.com/ngrams/… – Adam Jun 23 '17 at 23:22
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Firstly "in terms of" isn't right usage. "xx grows yy with zz" is a more standard construction.

However, the relation you give in no ways implies it grows exponentially. It is not necessarily monotonically increasing. You can say it is bounded above and below by terms growing exponentially with h, but within that bound it may very well drop, undulate or have discontinuities.

If this is going in a math paper, precision is far more important than having good English usage.

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