Although deposits can expand many times, currency cannot
Since c>0, when the base money MB and checking deposits D increase, the inflation level does rise.
Any part of the increase in MB that is converted into an increase in currency does not have a multiplier effect. Therefore, only part of the increase in base money can achieve multiple expansion to support the expansion of check deposits.
Since e>0, any increase in base money and deposits results in higher excess reserves
In the case of a very high excess reserve ratio e, when $1 of deposits is converted into currency, the level of excess reserves drops significantly, freeing up some reserves to support more deposits and pushing the money multiplier upward.
Although the base money increased significantly during the quantitative easing process, the increase in money supply was much smaller because the money multiplier dropped by about 50% (the excess reserve ratio e increased unusually)