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13 Nov 2019
Question 1 (12 Marks) Newton's law of cooling states that the rate of change of temperature of an object, dr is proportional to the temperature difference between the object and its surroundings, (T - T.), where the constant of proportionality, k, is positive and depends on the object: dT--k(T-T.) dt Note that all temperatures in this questions are in degrees Centigrade, and times are in minutes. A cup of tea is made and satisfies T(0) = 95 and T(2) = 80, Assume that T, = 20. (a) Use the inear approximation to estimate k. (b) Use a suitable linear approximation to estimate T(5). (c) I like my tea at a temperature of T = 40, Use a linear approxination to tell me when I should drink my tea. d) Use the error term in the linear approximation in part (a) to provide an interval in which the constant k must lie.
Question 1 (12 Marks) Newton's law of cooling states that the rate of change of temperature of an object, dr is proportional to the temperature difference between the object and its surroundings, (T - T.), where the constant of proportionality, k, is positive and depends on the object: dT--k(T-T.) dt Note that all temperatures in this questions are in degrees Centigrade, and times are in minutes. A cup of tea is made and satisfies T(0) = 95 and T(2) = 80, Assume that T, = 20. (a) Use the inear approximation to estimate k. (b) Use a suitable linear approximation to estimate T(5). (c) I like my tea at a temperature of T = 40, Use a linear approxination to tell me when I should drink my tea. d) Use the error term in the linear approximation in part (a) to provide an interval in which the constant k must lie.
Beverley SmithLv2
19 May 2019