Question:Cesar is holding a barbecue party and he is cooking
hamburgers. However, he has colour blindness...
Question
Cesar is holding a barbecue party and he is cooking
hamburgers. However, he has colour blindness...
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 T be the
temperature of the hamburgers, t be the time in minutes after
placing hamburgers on the barbecue, H the temperature of the
barbecue, and k>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, and k. 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=1/10. Solve for T as an
explicit function of t, 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.