Exponential decay

Suppose a quantity q of substance is emitted by something over a period of time t, and the release is an exponential decay curve, like with cooling.

The proportion of q that has been emitted by an intermediate time h will be



\frac{{}1-e^{-(h/t)}} {1-e^{-1}}

( 1 - exp(-(h/t)) ) / ( 1 - exp(-1) )

The exponent -1 in the divisor is the reduction of -(1/1).

NB that we're saying nothing about whether more substance is emitted after the quantity q has been emitted. In particular the remaining amount of substance is unlikely to be 0 because the exponential decay curve never quite meets the x axis (I think).