studies have used measures of hyperbolic discounting to find that drug-dependent individuals discount delayed consequences more than matched nondependent controls, suggesting that extreme delay discounting is a fundamental behavioral process in drug dependence. Some evidence suggests pathological gamblers also discount delayed outcomes at higher rates than matched controls. Whether high rates of hyperbolic discounting precede addictions or vice versa is currently unknown, although some studies have reported that high-rate discounters are more likely to consume alcohol and cocaine than lower-rate discounters. Likewise, some have suggested that high-rate hyperbolic discounting makes unpredictable (gambling) outcomes more satisfying. The degree of discounting is vitally important in describing hyperbolic discounting, especially in the discounting of specific rewards such as money. The discounting of monetary rewards varies across age groups due to the varying discount rate. The rate depends on a variety of factors, including the species being observed, age, experience, and the amount of time needed to consume the reward. Mathematical model Step-by-step explanation Suppose that in a study, participants are offered the choice between taking x dollars immediately or taking y dollars n days later. Suppose further that one participant in that study employs exponential discounting and another employs hyperbolic discounting. Both participants know that they can invest the money they receive today in a savings plan that gives them an interest of r. Both of them realize that they should take x dollars immediately if the future value of the savings plan will yield more than y dollars n days later. Each participant correctly understands the fundamental question being asked: "For any given value of y dollars and n days, what is the minimum amount x of dollars, that I should be willing to accept? In other words, how many dollars would I need to invest today to get y dollars n days from now?" Each will take x dollars if x is greater than the answer that they calculate, and each will take y dollars n days from now if x is smaller than that answer. However, the methods that they use to calculate that amount and the answers that they get will be different, and only the exponential discounter will use the correct method and get a reliably correct result: The exponential discounter thinks "The savings plan adds to its value, in each day, r percent of the value that it had the previous day. So every day it multiplies