Final answer:
A retirement model can be described using differential equations, which are equations that relate functions and their derivatives. They can be used to model the time it takes for an individual to retire after reaching a certain age
Step-by-step explanation:
A retirement model can be described using differential equations. Differential equations are equations that relate functions and their derivatives. In the context of retirement, a differential equation can be used to model the time it takes for an individual to retire after reaching a certain age, such as age 60.
For example, if the time after age 60 to retirement is approximately exponentially distributed with a mean of 5 years, we can use a differential equation to model this distribution. The solution to this differential equation is called a logistic curve, which can be graphed to represent the probability distribution of retirement times.
By solving the differential equation and calculating probabilities, we can answer questions such as the probability that a person retired after age 70, whether more people retire before or after age 65, or how many people over age 80 have not yet retired in a room of 1,000.