# Math Help - calc 2 prob help

1. ## 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?

2. Originally Posted by twofortwo
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.