Need a MATLAB solution to this question. Please breakdown the code needed to solve this one. Thank you.

Problem 1 dT The rate of cooling of a body can be expressed as-=-k(T-Ta) dt k-a proportionality constant (per minute). Thus, this equation (called Newton's law of cooling) specifies that the rate of cooling is proportional to the difference in the temperatures of the body and of the surrounding medium. If a metal ball heated to 80 C is dropped into water that is held constant at Ta -20 C, the temperature of the ball changes, as in Time, min 5 10 15 20 25 T,T, C 80 44.5 30.0 24.21.7 20.7 Utilize numerical differentiation to determine dT/dt at each value of time. Plot dT/dt versus T Ta and employ linear regression to evaluate k Hint: cooling rate can be fit with a linear regression with zero intercept, find the function by yourself G