Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings. Suppose t is time, T is the temperature of the object, and Ts is the surrounding temperature. The following differential equation describes Newton's Law dT/dt =k(T?Ts) ,where k is a constant. Suppose that we consider a 92?C cup of coffee in a 20?C room. Suppose it is known that the coffee cools at a rate of 2?C/min. when it is 70?C Answer the following questions.1. Find the constant k in the differential equation. Answer (in per minute): k= 2. What is the limiting value of the temperature? Answer (in Celsius): T= 3. Use Euler's method with step size h=2 minutes to estimate the temperature of the coffee after 10 minutes. Answer (in Celsius): T(10)?

Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings. Suppose t is time, T is the temperature of the object, and T's is the surrounding temperature. The following differential equation describes Newton's Law dT = K(T - T.) , dt where k is a constant. Suppose that we consider a 92"C cup of coffee in a 20*C room. Suppose it is known that the coffee cools at a rate of 2 C/min. when it is 70"C. Answer the following questions. 1. Find the constant k in the differential equation. Answer (in per minute): k = 2. What is the limiting value of the temperature? Answer (in Celsius): T = 3. Use Euler's method with step size h = 2 minutes to estimate the temperature of the coffee after 10 minutes. Answer (in Celsius): T(10) =