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Math Help - calc 2 prob help

  1. #1
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    calc 2 prob help

    A cup of hot chocolate is initially 170F and is left in a room with ambient temperature of 70F. suppose tht at time t=0, it is cooling at a rate of 20 degrees per minute
    Assume that newtons law of cooling applies: the rate of cooling is portortional to the difference between the current termperate and the ambient temperature
    how long does it take the hot chocolate to cool to a temperate of 110 F?
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    Quote Originally Posted by twofortwo View Post
    A cup of hot chocolate is initially 170F and is left in a room with ambient temperature of 70F. suppose tht at time t=0, it is cooling at a rate of 20 degrees per minute
    Assume that newtons law of cooling applies: the rate of cooling is portortional to the difference between the current termperate and the ambient temperature
    how long does it take the hot chocolate to cool to a temperate of 110 F?
    let y = temp of the drink in deg F at any time t in minutes

    \frac{dy}{dt} = k(y - 70)

    you are given that \frac{dy}{dt} = -20 deg/min at t = 0 ... use this info to find the proportionality constant, then solve the DE for y as a function of t.
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