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An object is heated to 90 degrees Celcius and is then allowed to cool in a room whose air temperature is 25 degrees celcius. If the temperature of the object is 75 degrees celcius after 10 minutes, when will its temperature be 50 degrees celcius?

  • Math -

    You will need Newton's Law of Cooling formula, which is
    T(t) = Tm + (T0 - Tm)e^(kt)

    where T(t) is the current temperature of the object
    Tm is the surrounding temperature and
    T0is the starting temperature
    t is in minutes, and k is a constant

    first we have to find the value of k

    75 = 25 + (90-25)e^(10k)
    50 = 65 e^(10k)
    .76923 = e^(10k)
    10k = ln .76923
    k = -.026236

    so now
    50 = 25 + (90-25)e^(-.026236t)
    25/65 = e^(-.026236t)
    (-.026236t) = ln(25/65)
    t = 36.42 minutes

  • Math -

    Thank you!!!

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