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Math Help - brain teaser

  1. #1
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    Apr 2009
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    brain teaser

    I'm totally lost here!!

    Your team has been called in to solve a problem encountered by a fast food restaurant. They believe that their coffee should be brewed at 170 deg Fahrenheit. However, at temperature it is too hot to drink, and a customer who accidentally spills the coffee on himself might receive third degree burns.

    What they need is a special container that will heat the water to 170 deg, brew the coffee at that temperature, then cool it quickly to a drinkable temperature, say 140 deg F and hold it there, or at least keep it at or above 120 deg F for a reasonable period of time without further cooking. Yo cool down the coffee, 3 companies have submitted proposals with these specifications.

    a)the Centikeeper Company has a container that will reduce the temperature of a liquid from 200 deg F to 100 deg F in 90mins by maintaining a constant temperature of 70deg F

    B)The TempControl Company has a container that will reduce the temperature of a liquid from 200deg F to 110deg F in 60mins by maintaining a constant temperature of 60deg F.

    C)the hot n cold Inc. has a container that will reduce the temperature of a liquid from 210deg F to 90deg F in 30mins by maintaining a constant temperature of 50deg F.

    Your job is to make a recommendation as to which container to purchase . For this you will need Newton's Law of Cooling, whick follows:
    u(t)=T+(u base 0 - T)e^kt k<0

    In this formula,
    T represents the temperature of the surrounding medium
    u base 0 is the initial temperature of the heated object
    t is the length of time in minutes
    k is a negative constant
    u represents the temperature at time t

    1)Use Newtons's law of cooling to find the constant k of the formula for each container
    2)Use a graphing utility to graph each relation.
    3)How long does it take each container to lower the coffee temperature from 170deg F to 140deg F
    4)How long will the coffee temperature remain between 120deg F and 140deg F
    5)On the basis of this information, whick company should get the contract with McNewton's? What are your reasons?
    6)Define "capital cost" and "operating cost". How might they affect your choice?
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  2. #2
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  3. #3
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    thanks...
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