Is this the right formula to use?

it provides an alternative energy pathway for the reaction to proceed.

a catalyst is a substance that speeds up the rate of a chemical reaction but is not consumed during the course of the reaction.

catalysts increase the rate of reaction without being used up. they do this by lowering the activation energy needed. with a catalyst, more collisions result in a reaction, so the rate of reaction increases. different reactions need different catalysts.

a catalyst works by providing an alternative reaction pathway to the reaction product. the rate of the reaction is increased as this alternative route has a lower activation energy than the reaction route not mediated by the catalyst.