The super-standard expression is
exponential in n,
provided you understand that in many contexts, it includes a broader range of functions than just the one you've written. Basically, exponential in n means that the 'dominant scaling' with n is exponential. For example, for every one of the following functions, there are fields where it would be described as 'exponential in n' (or in k, or in d… , as the case may be):
2n/log n (' exponential in n ')
In Nielsen, Michael A. Nielsen, Isaac L. Chuang, Quantum Computation and Quantum Information, 2000 (link)
2k+1 k log k (' exponential in k ')
In Advances in Neural Information Processing Systems 15:
Proceedings of the 2002 Conference (link)
qd2 (' exponential in d '; yes, they say d, not d2)
In Aspects of Complexity: Minicourses in Algorithmics, Complexity and Computational Algebra: Mathematics Workshop, Kaikoura, January 7-15, 2000 (link)
It is not an accident that all these are in complexity-related fields. When judging whether a quantity is 'exponential' in a parameter, all that the practitioners in these fields care about is that the parameter enters some exponent, and that the way it enters the exponent is significantly faster than logarithmic. (After all, the logarithm can 'cancel out' the exponential: eln x = x.)
Having said that, in some fields, the usage is stricter. For example, the 2n log n scaling is referred to as super-exponential here, while any scaling 2o(n) is called sub-exponential here (where the 'little o notation' is being used: f(n) = o(n) as n → ∞ means that that f(n)/n → 0 in that limit). No doubt, there are many fields where 'y is exponential in n' could only mean that y = a bn for some a and positive b. But since we don't know the relevant field (you may!), we can't exclude the possibility that the meaning of 'exponential in (a parameter)' is as broad as in the examples I gave above.
If you want to forestall this broad interpretation, you will have to rephrase and use a longer description, e.g.
y is proportional to the exponential function of a constant multiple of n.