The thick red line shows the subjective present value of 120 pounds. The straight lines show its value at t=1 and t=6. The thick green line shows the subjective present value of 100 pounds. The straight green lines highlight its value at t=5. The slider controls the subject's sensitivity to time.
With exponential discounting, one additional year has the same effect, no matter whether that's one year from the present, or one year in the future. An exponential discounter would rather have £100 now than £120 in a year's time if and only if they'd rather have £100 in five years than wait an additional year to get £120.
Hyperbolic discounters don't behave that way. By translating a choice to a different point in the future, it is possible to get a preference reversal. For example, a hyperbolic subject might much prefer £100 now to £120 in a year's time, but value £100 in five years less than waiting one more year to get £120.
This page by Martin Poulter of the Economics Network is released under a Creative Commons by-nc licence.
See also Hyperbolic versus exponential discounting