Consider the DTDS M++1 = M₁er (2-(Mt/3)) where r > 0 is a parameter (which may appear in your answers). a) Find the updating function f. Answer: f(M) = b) Calculate the positive equilibrium M*. Answer: M* = c) Compute the derivative of the updating function with respect to M. Answer: f' (M) = d) Determine the range of values of r for which the positive equilibrium M* is stable. Give exact values. Answer: Number <r< Number