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For the radioactive isotope decay, you know that , where is some decay constant. describes the number of decays per second of the radioactive isotope to the stable product, in other words,
in self-explanatorily. The negative sign should be obvious- you're losing radioactive isotope. Anyhow, you know that for every radioactive decay, you gain one stable product- can you think of a way to relate to ? Try to put that into the equation above and get an integral going to get .