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Math Help - Need Help Writing Math Problem As Expression

  1. #1
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    Smile Need Help Writing Math Problem As Expression

    Hello, I need help with the following math problem. It needs to be written as an expression.

    Problem: An experiment is underway to test the effect of extreme temperatures on a newly developed liquid. Two hours into the experiment the temperature of the liquid is measured to be -17 degrees celsius. After eight hours of the experiment, the temp. of the liquid is -47 degrees celsius. Assume that the temperature has been changing at a constant rate throughout the experiment and will continue to do so.


    Any help with this problem will be greatly appreciated.

    Thanks!
    David
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  2. #2
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    Hello, David!

    An experiment tests the effect of extreme temperatures on a liquid.
    Two hours into the experiment, the temperature of the liquid is -17 C.
    After eight hours of the experiment, the temp. of the liquid is -47 C.

    Assume that the temperature has been changing at a constant rate
    throughout the experiment and will continue to do so.

    Write an expression for this experiment.

    Since the change is constant, we have a linear function: .y .= .ax + b

    . . When x = 2, y = -17: . -17 .= .2a + b

    . . When x = 8, y = -47: . -47 .= .8a + b


    We have a system of equations: . [1] .2a + b .= .-17
    . . . . . . . . . . . . . . . . . . . . . . . . [2] .8a + b .= .-47

    Subtract [1] from [2]: . 6a = -30 . . a = -5

    Substitute into [1]: . 2(-5) + b .= .-17 . . b = -7


    Therefore, the function is: . y .= .-5x - 7

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  3. #3
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    Quote Originally Posted by David7299 View Post
    Hello, I need help with the following math problem. It needs to be written as an expression.

    Problem: An experiment is underway to test the effect of extreme temperatures on a newly developed liquid. Two hours into the experiment the temperature of the liquid is measured to be -17 degrees celsius. After eight hours of the experiment, the temp. of the liquid is -47 degrees celsius. Assume that the temperature has been changing at a constant rate throughout the experiment and will continue to do so....
    Hello David,

    I'm not quite certain whether I understand this problem right or not.

    If the rate of changing is constant then you have to do with an exponential function:

    Let T(t) be the temperature at the time t. T_0 is the temperature at the time t = 0.

    T(t)=T_0 * e^(k * t)
    Be careful not to mix the different tT's.

    You know: T(2) = -17C and T(8) = -47C. Plug in these values into the equation:

    -17=T_0 * e^(k * 2)
    -47=T_0 * e^(k * 8)

    From the first equation you can calculate T_0 = (-17)/(e^(2k)). Plug in this result into the 2nd equation and you'll get k = (ln(47)-ln(17))/6 ≈ 0.16945.

    And T_0 ≈ -12.112C.

    Now you can assemble all these results to an equation:

    T(t) = -12.112 * e^(0.16945 * t)

    EB
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  4. #4
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    Thumbs up Thanks for the help

    I want to thank both of you so much. It helped me out alot. Thanks for taking the time out and helping. Sincerely, David
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