Question: Suppose that an object with an initial temperature T 0 is placed in an atmosphere of temperature T a . Newton's Law of Cooling states

Suppose that an object with an initial temperature T₀ is placed in an atmosphere of temperature T_a. Newton's Law of Cooling states that the temperature of the object after t minutes is given by the function T(t) = T_a + (T₀ - T_a) e^-kt, where k is a positive constant that depends on the type of object.

a) A restaurant serves a cup of coffee at a temperature of 190^oF. If the manager of the restaurant keeps the thermostat set at 68^oF, what will the temperature of the coffee after 30 minutes if no one drinks it? (Assume that k = 0.075) Include units

b) At the same restaurant, a bowl of chili is served at 182^oF. If a customer can't eat it at a temperature higher than 108^oF, how long will he need to wait? (Assume that k = 0.012) Include units

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