1. The problem statement, all variables and given/known data a) An object at 200 degrees F is put in a room at 60 degrees F.The temperature of the room decreases at the constant rate of 1 degree every 10 minutes. The body cools to 120 degrees F in 30 minutes. How long will it take for the body to cool to 90 degrees F? b) Show that the solution of the pertinent initial value problem which models the situation is: T(t) = 60 + 140e^(kt) + [(e^(kt) - kt - 1)/(10k)] c) Set-up an equation from which you can solve for k. d) Set-up an equation from which the required cooling time can be found. 2. Relevant equations Newton's Law of Cooling: T'(t) = K(T(t) - T0) Note: T is in minutes 3. The attempt at a solution a) This is variable seperable dT/dt = K(T(t) - T0) ∫dT/(T(t) - T0) = ∫k dt + C ln (T(t) - T0) = kt + C (T(t) - T0) = ce^(kt) T(t) = ce^(kt) + T0 At T(0) = 200, and T0 = 60 200 = ce^(K*0) + 60 c = 140 T(t) = 140e^(kt) + 60 This is where I get stuck. I'm not really sure where to go next. I'm mainly confused by the fact that room temperature is decreasing as well.