![]() ![]() But regardless of the substance, when we’re looking at half life, we know thatīecause ?y? is the amount of substance that remains as the substance decays, and because ?C? is the amount of substance we started with originally, when the substance has decayed to half of its original amount, ?y? will be equivalent to ?C/2?. Because every substance decays at a different rate, each substance will have a different half life. Since substances decay at different rates, ?k? will vary depending on the substance.Įvery decaying substance has its own half life, because half life is the amount of time required for exactly half of our original substance to decay, leaving exactly half of what we started with. ![]() Where ?C? is the amount of a substance that we’re starting with, ?k? is the decay constant, and ?y? is the amount of the substance we have remaining after time ?t?. So, for now, we’ll just state that the basic equation for exponential decay is We won’t work through how to prove these formulas, because in addition to derivatives, we also use integrals to build them, and we won’t learn about integrals until later in calculus. ![]()
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