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.