Joan brings a cup of hot tea into a room and places the cup on a table. At time t minutes after Joan places the cup on the table, the temperature, θ°C, of the mug is modelled by the equation:
θ = 20 + Ae^{-kt}
where A and k are positive constants.
Given that the initial temperature of the tea was 90°C,
(a) Find the value of A.
The tea takes 5 minutes to decrease in temperature from 90°C to 55°C.
(b) Show that k = 1/5 ln 2.