A fast food restaurant wants a special container to hold coffee. The restaurant wishes to hold coffee. The restaurant wishes the container to quickly cool the coffee from 200 degrees to 130 degrees and keep the liquid between 110 degrees and 130 degrees as long as possible. The restaurant has three container to select from. 1. The Centikeeper Company has a container that reduces the temperature of a liquid from 200 degrees to 100 degrees in 20 minutes by maintaining a constant temperature of 70 degrees. 2. The TempControl Company has a container that reduces the temperature of a liquid from 200 degrees to 110 degrees in 25 minutes by maintaining a constant temperature of 60 degrees. 3. The Hot and Cold Company has a container that reduces the temperature of a liquid from 200 degrees to 120 degrees in 20 minutes by maintaining a constant temperature of 65 degrees. a) Use Newton's Law of Cooling to find a model relating the temperature of the liquid over time for each container. b) How ong does it take each container to lower the coffee temperature from 200 degrees to 130 degrees c) How long will the coffee temperature remain between 110 degrees and 130 degrees? This temperature is considered the optimal drinking temperature. e) Which company would you recommend to the restaurant? Why?