# The temperature is changing at a certain rate. What is the temperature when t=5?

1. ### lude1

34
1. The problem statement, all variables and given/known data

A pizza, heated to a temperature of 350 degrees Fahrenheit, is taken out of an oven and placed in a 75°F room at time t=0 minutes. The temperature of the pizza is changed 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?

2. Relevant equations

f'(t) = -ky?
All I can think of is that this problem is related to Newton's Law of Cooling.

3. The attempt at a solution

The rate of change or derivative is -110e-0.4t. I think what you're suppose to do is find how much the temperature dropped and subtract this number to the original temperature, 350°. I originally thought, if I plugged in t=5 into
-110e-0.4t and subtract this number from 350°, then I would have my answer. But, of course, this is wrong.

2. ### rock.freak667

6,231
So we have this meaning that

dT/dt = -110e-0.4t ⇒ T= ∫(dT/dt) dt

So what is T equal to?