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Math Help - Coffee problem! Please help immediately!

  1. #1
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    Coffee problem! Please help immediately!

    At time t=0 minutes, the temperature of a cup of coffee is 180 degrees fahrenheit. Left in a room whose temperature is 70 degrees Fahrenheit, the coffee cools so that its temperature function T(t), also measure in degrees Fahrenheit, the differential equation dT/dt = -1/2T + 35

    a) Find an expression for T(t) using the initial condition T(0)=180

    c) At what time t is the temperature of the coffee decreasing at the rate of 15 degrees Fahrenheit per minute? How hot is the coffee at that point? Indicate units of measurement.
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  2. #2
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    Re: Coffee problem! Please help immediately!

    Hey lysskli.

    Hint: You have a separable DE where dT/[-0.5T + 35] = dt. This means you can integrate and collect terms to get T(t) = f(t) for some function f. What do you think the anti-derivative of 1/(-0.5T + a) will be (where a is a constant)?
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  3. #3
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    Re: Coffee problem! Please help immediately!

    I honestly don't know. Do I take the integral?
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  4. #4
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    Re: Coffee problem! Please help immediately!

    Yes integrate both sides: one side will be in terms of dT and the other in terms of dt. Once you do that then get T as a function of t and you're done.
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  5. #5
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    Re: Coffee problem! Please help immediately!

    Quote Originally Posted by lysskli View Post
    I honestly don't know. Do I take the integral?
    What you have is (with some abuse of notation etc) is:

    \frac{dt}{dT}=\frac{1}{-0.5T+35}

    which you could try integrating...

    .
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