A thermometer is removed from a room where the temperature is 70° F and taken outside, where the air temperature is 10° F. After a half a minute the thermometer reads 50° F. What is the reading of the thermometer at t = 1 minute? How long will it take for the reading on the thermometer to reach 15° F? Solve the problem as follows: a) construct a linear first-order DE that models the behaviour of Newton's Law of Cooling and state the initial condition; b) solve the DE and find the constant k using the fact that at half a minute the thermometer reads 50° F; c) what will the temperature T, be at t = 1 minute; d) how long will it take the thermometer to display a reading of 15° F; e) sketch a rough graph of the solution in Question 3 (b) which displays the behaviour of the thermometer readings over time. Label the axes and relevant points on the graph;

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