A cup of soup cools to the temperature of the surrounding air. Newton's law of cooling can be written as T - T_s = (T_0 - T_s)e^-kt where T is the temperature of the object after t minutes, and T_s is the temperature of the surrounding air. The soup cooled from 90° C to 70° C after 6 minutes in a room with an air temperature of 15° C.

Question

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Find the values of T_s, T_0 and k correct to 2 decimal places

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b) write the equation substituting the values for T_s, T_0 and k

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c) find the temperature of the soup after 10 minutes. Give your answer to the nearest degree

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d) how long would it take for the soup to be 40° C? Give your answer to the nearest minute

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e) if the soup is placed in a refrigerator in which the temperature is 2° C, how long will it take for the soup to reach 40° C? Use the same value of k and give your answer to the nearest minute

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