### 4.2.6 Solution of the difference equation

If we assume that the fish population P = P0 at time t = t0, then the equation

has the standard solution

Pt = P0.(1+k)t

as can easily be verified by direct substitution.

As an aside we can take the time period to be, say one year. If we apply the same ideas to a time period of six months, the basic equation is

and so

In a similar fashion, we can obtain the equation

corresponding to a monthly application, and

corresponding to a daily application.

You should be able to deduce the answer corresponding to an infinitely small time interval from the above information.