# Law of cooling and Exponential growth

1. Oct 9, 2007

### fk378

1. The problem statement, all variables and given/known data
A roast turkey is taken from an oven when its temperature has reached 185 degrees F and is placed on a table in a room where the temperature is 75 degrees F. When will the turkey have cooled to 100 degrees F?

2. Relevant equations
dT/dt=k(T-Ts) where Ts=temperature of the surrounding
y(t)=y(0)e^kt

3. The attempt at a solution
I solved T(t)=75+110e^(ln .682)t/30

Solving for t:
100=75+110e^(ln .682)t/30
t=10

I know that t=10 isn't right, but I don't know what I did wrong. Any takers?

2. Oct 9, 2007

### dashkin111

How did you solve for k?

Just quickly I got:

$$\frac{1}{k}ln(\frac{25}{110})$$

3. Oct 9, 2007

### fk378

To solve for k I used the fact that y(30)=150-75=75
So, 110e^30k=75
e^30k=.682
30k=ln .682
k= ln .682/30

4. Oct 10, 2007

### HallsofIvy

Staff Emeritus
And how did you know that y(30)= 75? You didn't tell us anything about the temperature of the turkey 30 minutes after being take out of the oven!

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?