A discount function is used in economic models to describe the weights placed on rewards received at different points in time. For example, if time is discrete and utility is time-separable, with the discount function having a negative first derivative and with (or in continuous time) defined as consumption at time t, total utility from an infinite stream of consumption is given by
Total utility in the continuous-time case is given by
provided that this integral exists.
Exponential discounting and hyperbolic discounting are the two most commonly used examples.