You see, in a first order reaction, the half-life is a fixed constant from the mathematics, like a clock ticking down regardless of how much you start with—it's built into the formula t½ = ln(2)/k. But in our factory, when we test a product's degradation, the theory says it shouldn't depend on the initial amount, yet my measurements for 99% completion never quite match the book because the real 'k' changes with our erratic town voltage affecting the stability chamber. So, while the professor's derivation is perfect, my old meters and the summer heat make me doubt it in practice.
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