I have a difference equation which is given as: ΔP = e^P  where we can re-write ΔP as: Δ P = P_2 - P_1, where the subscripts indicate two distinct discrete time indices. What I would like to do: is to convert this into a continuous time expression and solve it, if possible. In order to help give some insight, I will solve a similar type of problem where I know the solution. ΔP = c_1  Note here, that in all cases we are running the recursive algorithm at a fixed data rate. Therefore, I can rewrite equation  as: Δ P = P_2 - P_1 = c_2 ⋅ Δ t where c_1 = c_2 ⋅ Δ t This allows me to divide both sides by [equation] \Delta t [/equation]: ΔP /Δt = c_2 And in the limit: dP/dt = c_2 which then becomes: P(t) - P(0) = c_2⋅(t - t_0) And so the result is that this recursive equation  gives us a linear ramp if we were to implement it. What I am trying to do for equation  is figure out what this expression will look like.