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(a) A cup of coffee has temperature 95 $ ^\circ C $ and takes 30 minutes to cool to 61 $ ^\circ C $ in a room with temperature 20 $ ^\circ C $. Use Newton's Law of Cooling (section 3.8) to show that the temperature of the coffee after $ t $ minutes is
$$ T(t) = 20 + 75 e^{-kt} $$
where $ k \approx 0.02 $.
(b) What is the average temperature of the coffee during the first half hour?
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