The brewing temperature of the water used is very important. It should be between 195 F and 205 F. The closer to 205 F the better. Boiling water (212 F) should never be used, as it will burn the coffee. Water that is less than 195 F will not extract properly. On the other hand, coffe that has a temperature of 205 F is too hot to drink. 6 Coffee best when it is served at a temperature of 140 F to 155 F (the Goldilocks range). (a) Suppose coffee is initially brewed at 205 F. If room temperature is 70 F, set up an initial-value problem to model the temperature of the coffee at time t, where t is the time in minutes after brewing has finished.
(b) Solve the initial-value problem from Task 1.2.2.a
(c) If the temperature of the coffee drops from 205 F to 200 F in the first two minutes after brewing, how long before the coffee reaches a temperature of 155 F?