Problem 1. (25 pts) Use the AE5031_HMW1_1.m code to solve the ODE df/dt = -f, f(0) = 1. a) [5 pts] Find the exact solution. b) [10 pts] Use the code for various timesteps 4t and calculate the error= | Exact- Numerical/Exact as a function of the Dt at time time t = 1. c) [10 pts] Plot the error versus the At on a logarithmic scale to confirm that the error decreases proportionally to the 4t (1st order accuracy)

Fig: 1