Consider the non-linear system of odes given by yí = fı (y1, y2) = yỉ + 3y172, y = f2 (y1, y2) = 2yı + yż. find all of the critical points of the system, calculate the linearized system about each of the critical points found and classify the type of critical point in each of the linearized systems. plot a phase portrait for the non-linear system by hand. (15 marks)

The federal reserve controls certain interest rates in the united states. investors often try to speculate as to whether the federal reserve will raise or lower rates and by how much. suppose a company conducts extensive interviews with financial analysts, and as a result, predicts that "thefed" will increase rates by an average of 0.25 percentage points every six months for the forseeable future. which type of equation could be used to model the predicted interest rates over the next several years, assuming no other significant changes? a) a linear equation b) a quadratic equation c) a polynomial equation d) an exponential equation