Final answer:
The decomposition reaction in question, with a half-life directly proportional to the initial concentration of the reactant, is a zero-order reaction.
Step-by-step explanation:
A student has asked about the order of a decomposition reaction where the half-life is directly proportional to the initial concentration of the reactant. In chemistry, the relationship between the half-life of a reaction and the concentration of the reactants is characteristic of the reaction order. For a first-order reaction, the half-life is independent of the initial concentration, which is not the case here. Whereas, the half-life of a zero-order reaction increases as the initial concentration of the reactant increases. Therefore, if the half-life of the decomposition reaction is directly proportional to the initial concentration, the reaction is of zero-order.