The effect of a catalyst in a chemical reaction is to increase the rate of a reaction by changing the pathway or mechanism of the reaction and/or to lower the transition state's energy thereby lowering the activation energy of the reaction
The pathway of the reaction is changed by the catalyst by the formation of intermediate compounds by the catalyst which require lower activation energy to form the products than the original non-catalyzed reactants. In the process the catalyst is regenerated, thereby, not taking part in the reaction.
If a sample has decayed to 25%, this means 2 half-lives have passed. We are given this is equal to 7 yrs, and it follows that one half life is 3.5 yrs.
