17. The National Coffee Association of USA recommends that the temperature of coffee must be between 82.2 °C and 85 °C for optimal flavor notes. A cup of coffee is served at 95 °C in room with temperature 20 °C. (a) Using Newton's Law of Cooling and time in minutes, with decay constant k, set up a differential equation and solve it to show why the temperature of the coffee can be modeled by the function y(t) = 20 + 75ekt. (b) Five minutes after it's served, the coffee cooled down to 90 °C. Determine the decay constant k. Round to two significant digits (3 decimal places). (c) Using the answers in (a) and (b), determine the time interval in which the coffee should be ideally consumed. Round your answers to 2 decimal places.

17. The National Coffee Association of USA recommends that the temperature of coffee must be between 82.2 °C and 85 °C for optimal flavor notes. A cup of coffee is served at 95 °C in room with temperature 20 °C. (a) Using Newton's Law of Cooling and time in minutes, with decay constant k, set up a differential equation and solve it to show why the temperature of the coffee can be modeled by the function y(t) = 20 + 75ekt. (b) Five minutes after it's served, the coffee cooled down to 90 °C. Determine the decay constant k. Round to two significant digits (3 decimal places). (c) Using the answers in (a) and (b), determine the time interval in which the coffee should be ideally consumed. Round your answers to 2 decimal places.