. (20 pts) Code in MATLAB: An airfoil is placed in a wind tunnel, is heated to 80C and then the temperature of the surface of the airfoil is lowered to 20.7C using convective cooling. A thermocouple is placed on the surface of the airfoil and is used to measure the temperature at discrete time steps. The following temperatures are recorded: Time (t)0510 15 20 25 TC 80 44.5 30 24.1 21.7 20.7 a. Use the 3 numerical differentiation techniques to calculate dT/dt at each time step. Specifically, use 3 point forward, 3 point backward and 3 point central difference wer ever appropriate. Store the derivative dT/dt at each time step in a vector b. The rate of cooling of a body can be modeled using the following expression dT dt where T is the temperature of the body (C), Ta is the temperature of the surrounding medium (eC) and k is an unknown proportionality constant. This equation is known as dT dt ewton's Law O use thevector created in the previous step and the least squares method to calculate the proportionality constantk