Consider a 4-lb roast initially taken out of the refrigerator at 50^o F and is placed in a 375^o oven, compute how long it would take for the roast to reach 160^o F (fully cooked). After 75 minutes of cooking, its found that the roast temperature is 125^o F. (Note: k=0.0035) Write a program that will provide a simulation of the roasts temperature until it reaches (or exceeds 160o F) for three time increments, i) dt=30min, ii) dt=15min, and iii) dt = 5 min as well as the exact solution (derived in class). How long does it take for the roast to be fully cooked (>160^o F)? Output results: Generate one graph that shows all three test cases. Time to reach fully cooked state.

In Matlab.