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Half time is the time taken by a quantity to reach one half of its extremal value, where the rate of change is proportional to the difference between the present value and the extremal value. It is synonymous with half-life, but used in slightly different contexts.
The diagram shows the increase in the quantity in response to a step-change in the motive force that changes it. The time-axis is in multiples of the half time. It can be seen that the quantity increases to one-half of its final value after one half time, to three-quarters after two half times, to seven-eighths after three half times, and so on.
The relationship between the quantity and time is described by the mathematical formula:
where Qf is the extremal value and λ is a constant, approximately equal to 0.69 divided by the half time – more precisely: loge /.