Celeste heated a cup of coffee and then let it cool to room temperature. Celeste found the coffee's temperature, T, measured in °C, could be modelled by the following function, T(t) = 71e^-0.0514t + 23, t ≥ 0, where t is the time, in minutes, after the coffee started to cool.
(a) Find the coffee's temperature 16 minutes after it started to cool.
The graph of T has a horizontal asymptote.
(b) Write down the equation of the horizontal asymptote.
(c) Write down the room temperature.
(d) Given that T^-1(50) = k, find the value of k.