Question

Cesar is holding a barbecue party and he is cooking hamburgers. However, he has colour blindness and cannot tell whether the burger patties are cooked just by looking. Fortunately he remembers Newton's Law of Heating and Cooling.

Recall that this Law states that "The rate of change of the temperature of an object is proportional to the difference between the current temperature of the object and the ambient temperature."

Let TT be the temperature of the hamburgers, tt be the time in minutes after placing hamburgers on the barbecue, HH the temperature of the barbecue, and k>0k>0 the positive constant of proportionality.

a) (4 points) Write the differential equation stating Newton's Law of Heating and Cooling in terms of T(t),t,H,T(t),t,H, and kk.

Put your answer in a box. No explanation is required.

b) (5 points) Suppose the barbecue is at a temperature of 400F, the hamburger patties have been in the refrigerator at a temperature of 40F, and the constant of proportionality has a value of k=1/10k=1/10.

Solve for TT as an explicit function of tt, assuming the patties were placed in the barbecue immediately after being taken out of the refrigerator. Be sure to show all of the steps in your solution, rather than using a memorized formula.

Answer 1