Newton's Law of Cooling is based on the principle that the rateof change of temperature y'(t) of a body in an environment withambient temperature A is proportional to the difference b/w thetemperature y(t) of the body and the ambient temperature A, so thaty'=k(A-y) for some constant k.
(1) Sketch the direction field for the equation y'=K(A-y) fork=1/10 and A=70degrees. Then sketch several solution curves basedon starting values of y(0) both greater than and less than A.Discuss the implication of your graph in general, and as it relatesto the long-term limiting temperature of a cup of hot coffeeinitially at 190degreeF and a cup of iced coffee initially at40degreesF in a room with ambient temperature 70degreesF.
