In difference equation models, the difference in the quantity of interest can result from a net gain or loss in absolute terms, an amount, or relative to the present value of the quantity. In practice amounts in and amounts out add up to a net amount in or out and rates in and rates out likewise net out to a single rate in or out. This is the logic that let's us write a general difference equation as

\begin{equation} P_{n+1} = a P_{n} + b \end{equation}

where a is the net rate and b is the net amount.

If we start with that distinction between amounts and rates, there are four basic types of difference equations, two simple and two mixed:

Type Description Example Equation
Simple amount in and amount out College enrollment, new recruits, graduates $Enrollment_{i} = Enrollment_{i-1} + Recruits - Graduates$
Simple rate in and rate out Population with a birth rate and a death rate $Population_{i} = Population_{i-1} + Population_{i-1} \times BirthRate - Population_{i-1} \times DeatRate$
Mixed amount in and rate out Reservoir, rainfall, leakage $Reservoir_{i} = Reservoir_{i-1} + RainFall - Reservoir_{i-1} \times LeakageRate$
Mixed rate in and amount out Endowment, interest, expenditure $Endowment_{i} = Endowment_{i-1} + Endowment_{i-1} \times InterestRate - AnnualEndowmentExpenditure$