# 4) A fast-food restaurant wants a special container to hold coffee.

4) A fast-food restaurant wants a special container to hold coffee. The restaurant wishes thecontainer to quickly cool the coffee from 200°F to 130°F and keep the liquid between 110° and130°F as long as possible. The restaurant has three containers to select from.The CentiKeeper Company has a container that reduces the temperature of a liquid from 200°Fto 100°F in 30 minutes by maintaining a constant temperature of 70°F.The TempControl Company has a container that reduces the temperature of a liquid from 200°Fto 110°F in 25 minutes by maintaining a constant temperature of 60°F.The Hot’n’Cold Company has a container that reduces the temperature of a liquid from 200°Fto 120°F in 20 minutes by maintaining a constant temperature of 65°F.You need to recommend which container the restaurant should purchase.a) Use Newton’s Law of Cooling to find a function for each of the containers above relatingthe temperature of the liquid over time. (That is, the independent variable is time inminutes and the dependent variable is temperature in degrees Fahrenheit.)b) Graph all three functions on a single set of axes. Color code each graph, and include alegend to identify each graph by color.c) How long does it take each container to lower the coffee temperature from 200°F to130°F?d) How long will the coffee temperature remain between 110°F and 130°F? Thistemperature is considered the optimal drinking temperature.e) Which company would you recommend to the restaurant? Why?f) How might the cost of the container affect your decision?