As usual, apply the SNR equation:
Thus we see that increasing the image size by a factor of two (same matrix size but half the FOV dimensions), decreases the SNR by a factor of four. Doubling the resolution (doubling the matrix size Nx.Ny) yields a decrease of SNR by a factor of 2, as well as causing an increase in scan time.
Regarding scan time: consider reducing the FOV by a factor of two in both directions, and the slice thickness by a factor of 2. How much longer would we have to scan to maintain SNR (how many times must we multiply NEX (NSA))? Answer: sixty-four!