The First-order kinetic model can't be applied to experimental data. Instead, you have to check whether the experimental data are in agreement with the first reaction rate order with respect to A. This is a pretty complex protocol for the reaction with the stoichiometry such as,
aA + bB + cC = xX + yY + zZ
To simplify the procedure, you can use an excess of B and C. Then, you can assume that B and C does not change with time and you can write
dA/dt = F(Ao, Bo, Co) and check if A(t) = Ao(exp(-kt)). If this curve is exponential, you determine an apparent reaction rate constant k. If k does not depend on Ao, then you can say that the reaction is the pseudo first order with respect to A under conditions of your experiment. Pseudo means that k was determined under conditions Ao
I agree with Dr. Geletii but to certain extent. In fact the answer depends on the type of a reaction. If it is the interaction between several species then follow recommendations of Dr. Geletii, but if the reaction under study is, e.g., decomposition of a chemical then it easily can be of the 1st order and possibility to apply this model should be tested. Determining the effective reaction order on the basis of experimental data is another matter which requires special discussion.
Pseudo-first order reaction is reallty a second-order one but can be mathematically presented as a first-order one. It happens when one reactant is in a significant excess, and therefore its concentration is not changing during the course of the reaction like water in the hydrolytic processes.