Steve Marsden’s

This is known as the integrated rate law equation. No is the original amount of sample while N is the amount remaining at time t. This equation allows us to determine the decay rate of a sample at any given time AND to predict how much of a given sample will remain at any given time. It also shows that the rate behavior is logarithmic in nature.

Nuclear scientists often refer to the decay rate in terms of a quantity called half-life. This is simply the time it takes for half of a sample to decay into something else. The half-life can be related to the rate constant using the integrated rate law and recognizing that the ratio No/N will be 2/1 when t is the half-life: