Question

Newton’s Law of Cooling tells us that the time rate of chnge in temperature T(t) of a body immersed in a medium of constant temperature A is proportional to the difference A − T.The DE modeling this is dT dt = k(A − T). A cup of hot chocolate is initially 170◦ F and is left in a room with an ambient temperature of 70◦ F. Suppose that at time t = 0 it is cooling at a rate of 18◦ F per minute. (3 pts each part–show all work)

(a) Set up the differential equation that models the situation.

(c) Solve the equation you found in (a). Use the initial condition T(0) = 170 again to find the arbitrary constant. (d) Use (c) to find how long it takes for the temperature to be 110◦ F. (use Mathematica)

Answer 1