How Does This Exponential Price Increase Relate to the Concept of “Price Impact” on a Trade?
Price impact is the change in the asset's price caused by a trade. In the $x cdot y = k$ model, as a pool becomes unbalanced (one reserve is low), the price impact of any subsequent trade increases exponentially.
A small trade will require a disproportionately large amount of the other asset to maintain the constant $k$. This exponential price impact is the pool's mechanism to prevent total depletion and is the reason for high slippage in shallow or unbalanced pools.
