Problem 1: A mathematical model for the area A [cm'] that a colony of bacteria (B dendroides) occupies is given by, dA = A(2.128-0.0432A) dt Suppose that the initial area is 0.24 cm3. (a) Use the Runge-Kutta (RK4) method with h-0.5 [days] to complete the following table t [days] A (observed) A (approximated) 4 2.78 13.53 36.30 47.50 49.40 It is acceptable to use MS Excel or MATLAB to create a program that computes the values. Submit hand calculations and/or programs that shows all your work. Maintain a four-decimal approximation (b) Use separation of variables to solve the initial-value problem and compute the exact values: A), A(2), A(3), A(4), and A(5) (c) Use MS Excel or MATLAB to graph the solutions of the initial-value problem comparing the observed, approximated, and exact values