. A freshly brewed cup of coffee has a temperate of 95 degrees C. The cup is placed on a counter with surrounding temperature is 25 degrees C. Newton's law of cooling states that (dT)/(dt) = k(T - T_{s}) where T(t) is the temperature of the coffee at time t and is the surrounding temperature and k is a constant T_{s} based on the properties of the cup and the atmosphere. ( part a) Use Newton's law of cooling and the separation of variables method to derive an equation for T(t) . Your equation with contain k, but no constants of integration. ( part b) If the coffee has cooled to 50 degrees C after 10 minutes, find the value of k in part (a). ( part c) How long will it take the coffee to cool to 40 degrees C?

5. A freshly brewed cup of coffee has a temperate of 95 degrees C. The cup is placed on a counter with surrounding temperature is 25 degrees C. Newton's law of cooling states that dT dt = k(T - Ts) where T(t) is the temperature of the coffee at time t and Ts is the surrounding temperature and k is a constant based on the properties of the cup and the atmosphere. (a) Use Newton's law of cooling and the separation of variables method to derive an equation for T(t). Your equation with contain k, but no constants of integration. Math 2414 Test #3 (Final exam) Form A Summer 2022 (b) If the coffee has cooled to 50 degrees C after 10 minutes, find the value of k in part (a). (c) How long will it take the coffee to cool to 40 degrees C