A fast-food restaurant wants a special container to hold coffee. The restaurant wishes the container to...
A fast-food restaurant wants a special container to hold coffee. The restaurant wishes the container to quickly cool the coffee (due to a lawsuit!) from 200° to 130°F and keep the liquid between 110° and 130°F as long as possible. The restaurant has three containers to select from:
Option 1: The CentiKeeper Company has a container that reduces the temperature of a liquid from 200° to 100°F in 30 minutes by maintaining a constant temperature of 70°F.
Option 2: The TempControl Company has a container that reduces the temperature of a liquid from 200°F to 110°F in 25 minutes by maintaining a constant temperature of 60°F.
Option 3: The Hot’n’Cold Company has a container that reduces the temperature of a liquid from 200° to 120°F in 20 minutes by maintaining a constant temperature of 65°F.
You need to recommend which container the restaurant should purchase.
Isaac Newton developed a model stating that the temperature of a heated object decreases exponentially over time towards the temperature of the surrounding medium (environment).
This model is called Newton’s Law of Cooling and states: The temperature u of a heated object at a given time t can be modeled by the following function: u(t)=T+(u-T)e^kt. Where T is the constant temperature of the surrounding medium, 0 u is the initial temperature of the heated object, and k is a negative constant.
a. Use Newton’s Law to find a model for each option relating the temperature of the liquid over time for each container.
b. How long does it take each container to lower the coffee temperature from 200° to 130°F?
c. How long will the coffee temperature remain between 110° and 130°F for each model? This temperature is considered the optimal drinking temperature.
d. Graph each function using Desmos (link on elearning) with axes set to 0 40 ? ?t and 80 200 ? ? u . Include a printout of all three graphs on the same axes.
e. Which option would you recommend to the restaurant? Why?
f. How might the cost of the container affect your decision?
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A fast-food restaurant wants a special container to hold coffee.
The restaurant wishes the container to...
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