Help solve practice problem.

Newton's law of cooling says that the rate of change of temperature is proportional to the difference between the temperature T and the temperature of the surroundings, T, Solve the differential equation for a boiling kettle of water that is removed from the flame at 100"C and placed in a room that is at 20"C. t in minutes. Solve for T(t) explicitly. dT dt = k(T - T;) T(t) = What additional information would you need to be able to solve for "k"? Suppose a calculus student has that information finds that k = -0.07. Then the student uses the tangent line at t = 0 to estimate what temperature the kettle will cool to in 2 minutes. Find the second derivative aff ve or "(t) in terms of T(t). Use this to conclude whether the estimate is an overestimate or underestimate. d'T or T"(t) = (in terms of T) This is an because overestimate or underestimate