Kinetics is an experimental branch of chemistry. All rates of reactions and rate equations are determined from experimentation. Even if one did not know that Radioactive elements decay via first order kinetics one could determine this by observing the data and/or a graph of the decay of the element. If the 'concentration' (amount in the case of a solid) decreases by 50% in a specific time interval for each time interval then the reaction is following first order kinetics. Of course, statistics breaks down after a certain number of half-lives due to the sample size becoming rather small. So, a study of kinetics usually stops the data collection after fewer than 10 half-lives

Agree with those above. Radioactive decay is always first order. I tell my students to think of it this way, there is one reactant in a nuclear decay reaction. There is no way to predict when one atom will decay so we use half-life as the measure of rate of decay. Half of a sample will decay in this time period. Students should be able to determine from graph or data table.

Radioactive decay is one of the exemplar discussions for LO 4.3  In fact it is the only time decay is discussed in the entire CED.  Students need to be exposed to decay data as part of discussions on kinetics.

Radioactive decay is always a first-order process. First-order processes can often be identified from data or graphs by a constant half-life. Constant half-life (not dependent on concentration) = first order.

I think it's based on experimental evidence showing that reaction rate is proportional to reactant concentration (to a power of one). If you use the link below and scroll down to " Radioactive Decay Rates," it shows the derivation of the first-order rate equation. https://chem.libretexts.org/Textbook_Maps/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Nuclear_Chemistry/Nuclear_Kinetics/Half-Lives_and_Radioactive_Decay_Kinetics