How Is the Value of an LP Token Calculated When $k$ Changes Due to New Deposits?
The value of an LP token is calculated as the proportional share of the total assets in the pool. When a new deposit occurs, the total reserves ($x$ and $y$) and thus $k$ increase.
The number of new LP tokens minted is calculated such that the new LPs receive a share proportional to the value of their deposited assets, ensuring the value of existing LP tokens is not diluted. Trading fees also increase $k$, leading to a gradual appreciation in the value of existing LP tokens.
