Part C (Based off week 9 workshop content) In the last portfolio task, we modelled water draining from a tank with a small hole in the bottom. To slow the volume decrease of the tank, a hose is placed in the top of tank with flow rate Q(t). This results in the following modified Torcelli's law: dV dt 2gV (t) = Q(t)-a Given A = 4 m2, a = 0.1 m, g = 9.81 m/s, Q(t) 0.7e-0.1t mr/s and V(0) = 10 m, 1. Explain why this ODE cannot be solved analytically using separation or the integrating factor, 2. (AMS Submission) Write a MATLAB function that solves the ODE using MATLAB's ode45 from t = 0 to t = 50. 3. (AMS Submission) Create a MATLAB function that can numerically solve a first order ODE using the Modified Euler Method. The function should share the same inputs and outputs in the function declaration as the Euler Method Example covered in the week 8 lecture. 4. (AMS Submission) Using your code from Question 3, investigate the effect of the step size by solving the ODE using N - 10, 20, 40, 80. Plot all 4 numerical solutions and the ODE45 solution on the same figure, 5. Comment on the impact of halving step size (ie. doubling N) on the ac- curacy of the numerical solution. You can assume the ODE45 solution to be considered sufficiently exact in this comparison Part C (Based off week 9 workshop content) In the last portfolio task, we modelled water draining from a tank with a small hole in the bottom. To slow the volume decrease of the tank, a hose is placed in the top of tank with flow rate Q(t). This results in the following modified Torcelli's law: dV dt 2gV (t) = Q(t)-a Given A = 4 m2, a = 0.1 m, g = 9.81 m/s, Q(t) 0.7e-0.1t mr/s and V(0) = 10 m, 1. Explain why this ODE cannot be solved analytically using separation or the integrating factor, 2. (AMS Submission) Write a MATLAB function that solves the ODE using MATLAB's ode45 from t = 0 to t = 50. 3. (AMS Submission) Create a MATLAB function that can numerically solve a first order ODE using the Modified Euler Method. The function should share the same inputs and outputs in the function declaration as the Euler Method Example covered in the week 8 lecture. 4. (AMS Submission) Using your code from Question 3, investigate the effect of the step size by solving the ODE using N - 10, 20, 40, 80. Plot all 4 numerical solutions and the ODE45 solution on the same figure, 5. Comment on the impact of halving step size (ie. doubling N) on the ac- curacy of the numerical solution. You can assume the ODE45 solution to be considered sufficiently exact in this comparison