Bayesian Knowledge Tracing is used very widely to model student learning. It comes in two different forms: The first form is the Bayesian Knowledge Tracing "hidden Markov model" which predicts the probability of correct application of a skill as a function of the number of previous opportunities to apply that skill and the model parameters. We present an analytical solution to this model and show that it is, in fact, a function of three parameters and has the functional form of an exponential. The second form is the Knowledge Tracing "algorithm" which uses student performance at each opportunity to apply a skill to update the conditional probability that the student has learned that skill. We use a fixed point analysis to study solutions of this model and find a range of parameters where it has the desired behavior.