Law of cooling and Exponential growth

[fk378]

Homework Statement

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?

Homework Equations

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

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?

 

[dashkin111]

How did you solve for k?

Just quickly I got:

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

 

[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

 

[HallsofIvy]

How did you solve for k?

Just quickly I got:

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

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

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!