Table 3.  Some examples of first order linear difference equations.

Exploration

(i)  The exponential growth or decay model  

        has the solution  

    .  

(ii)  Newton's law of heating and cooling model  

        has the solution  

    .  

(iii)  The repeated dosage drug level model  

        has the solution  

    .  

(iv)  The value of an annuity due is the future value of all payments.  It is the sum of the compounded amounts for all payments.   It is given by the formula  

      
    
    

We can sum the series directly and get

When written as a difference equation we have
    
          
        or
          

This is a special case of the repeated dosage drug level model with  .

And Mathematica can solve the difference equation.

(c) 2006 John H. Mathews, Russell W. Howell