What exactly do you mean when you say the word model, because you sometimes refer to a graph or a mathimatical equation, and when you say model it doesn't specify which one you want, a graph or an equation?
The model is the function, which is represented by both the graph and the model.
The function can usually be expressed as a graph or an equation.
For example the depth vs. clock time function might be y = f(t) = .41 t^2 - 3.74 t + 94. The equation is y = .41 t^2 - 3.74 t + 94, and the graph represents this function.
The graph represents the equation, and the equation represents the graph, so the two are actually identical. The equation is generally more accurate than the graph, but within limits of accuracy the equation and the graph tell you exactly the same thing. What they both represent is the function.