Acore in an oil reservoir in town x at temperature 25° c is placed in a refrigerator where the ambient temperature f is 10° c. find the temperature of the core over a period of time. a standard way of approaching this type of problem is to break the time period into a number of small steps, each of length dt. if t; is the temperature at the beginning of step i, the updated temperature is given as ti+1 = ti - kdt(ti - f) where k is a constant parameter depending on the insulating properties of the core and the thermal properties of fluids present. assume that units are chosen so that time is in minutes. (a) write a function script called temperaturel. m that can (i) solve for the temperature profile, using 100 step values i. e. (i = 1 to 100), and time step, dt as 1, where dt = (i + 1) - i . the script should take input arguments t_ini (initial temperature), k and f; and an output argument of t. (ii) display the results of time and temperature for every 5 minutes in the following format time temperature 0 25. 5. 21.6067 (b) write a script named plt3.m that calls temperaturel. m to plot the temperature profile (temperature vs time) for k = 0.03, k = 0.05 and k = 0.15 on the same plot (nb. more complex plot styles get higher points.) (c) discuss your observations. hint: store the values of ti at every step into a vector and do same for time and plot both vectors for part (b).