We encountered a concrete example of such a difference equation in our discussion of interest rates and exponential growth. There, our `P` represented the bank balance (think principal), `Delta t` was the time between interest compoundings (one year in our example), and `k` was the interest rate for the compounding period (`0.005` in our original example). The upshot of our calculations was that the bank balance at time `t` could be represented by an exponential function with base `b=1+k`. In a Project that goes with this chapter, you will find that all solutions of difference equations of the form
are exponential functions, no matter what the time step or the proportionality constant.