Thread: Newton's Law of Cooling Question

A pizza, heated to a temperature of 350 degrees Fahrenheit is taken out of an oven and placed in a 75 degree room at time t = 0 minutes. The temperature of the pizza is changing at a rate of -110e^0.4t degrees Fahrenheit per minute. To the nearest degree, what is the temperature of the pizza at time t = 5 minutes?

I am not sure if I simply have to substitute in the time of 5 minutes and add it to the original temperature of 350 degrees, I've never done a question like this before. Could anyone help me out?

Originally Posted by xxlvh

A pizza, heated to a temperature of 350 degrees Fahrenheit is taken out of an oven and placed in a 75 degree room at time t = 0 minutes. The temperature of the pizza is changing at a rate of -110e^0.4t degrees Fahrenheit per minute. To the nearest degree, what is the temperature of the pizza at time t = 5 minutes?

I am not sure if I simply have to substitute in the time of 5 minutes and add it to the original temperature of 350 degrees, I've never done a question like this before. Could anyone help me out?

$\displaystyle \frac{df}{dt}=-110e^{-0.4t} $

get the antiderivative

$\displaystyle F(t) = - 110 e^{-0.4t}/-0.4 + F0$

$\displaystyle F(t) = 275 e^{-0.4t} + F0$

$\displaystyle 375 = 275(1) + F0$

$\displaystyle F0 = 100$

Becomes;

$\displaystyle
F(t) = 275 e^{-0.4t} + 100$

$\displaystyle F(5) = 275 e^{-0.4}(5) + 100$

$\displaystyle F(5) = 275 e^{-2} + 100$

I'm sure you can take it from here