Math

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?

asked by Hannah
  1. 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

    posted by Reiny
  2. Thank you!!!

    posted by Hannah

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