# Math Help - Newtons Law of Cooling

1. ## Newtons Law of Cooling

A cup of coffee was prepared at 90 degree C and left in a room at 20 degree C. Now the temperature is 60 degree and it is cooling at 1 degree/min. How much time has past since the coffee was made.
? netwons law ? dont know how to start it :S

2. let y = temperature at any time t

$\frac{dy}{dt} = k(y - 20)$

at $y = 60$ degrees, $\frac{dy}{dt} = -1$ deg/min

$-1 = k(60 - 20)$

$k = -\frac{1}{40}$

$\frac{dy}{dt} = k(y - 20)$

separate variables and solve for y as a function of t ... you have k and you also know y(0) = 90

3. ## thanks!

thank you so very much for the help now i can conntiue!