Hot Coffee A fast-food restaurant wants a special con- tainer to hold coffee. The restaurant wishes the container to quickly cool the coffee from 200 to 130F and keep the lig- uid between 110 and 130F as long as possible. The restau- rant has three containers to select from. 1. The CentiKeeper Company has a container that reduces the temperature of a liquid from 200 to 100F in 30 min- utes by maintaining a constant temperature of 70F. The TempControl Company has a container that reduces the temperature of a liquid from 200 to 110F in 25 min- utes by maintaining a constant temperature of 60F. The Hot'n'Cold Company has a container that reduces the temperature of a liquid from 200 to 120F in 20 min- utes by maintaining a constant temperature of 65F. You need to recommend which container the restaurant should purchase. (a) (b) (d) (e) (f) Use Newton's Law of Cooling to find a model relating the temperature of the liquid over time for each- container. How long does it take each container to lower the coffee temperature from 200 to 130F? How long will the coffee temperature remain between 110 and 130F? This temperature is considered the optimal drinking temperature. Graph each function using a graphing utility. Which company would you recommend to the restau- rant? Why? How might the cost of the container affect your decision