We present both analytical and numerical results for a model where the stochastic dynamical system is not fully known. We implement an optimal control solution for the problem that incorporates Bayes' learning of an unknown parameter in the model. The computational solution is for a model of phosphorus in a lake and we show that in that context full learning takes place. The model includes a Skiba-like point, and although the long run level of phosphorus in the lake is sensitive to initial conditions, learning is not.