This is what I have so far:Let's assume we find a dead body in a room with a constant temperature of 24 degrees.

At 8a.m, the body has a temperature of 28 degrees. At 9a.m it has a temperature of 26 degrees. Assuming normal body temperature is 37 degrees, when was the person killed?

$\displaystyle \frac{d \theta}{dt}=-k(\theta-\theta_0)$

I need to find k.

$\displaystyle \frac{d \theta}{dt_1}=-k(28-24)=-4k$

$\displaystyle \frac{d \theta}{dt_2}=-k(26-24)=-2k$

Both these equations give:

$\displaystyle \theta=-4kt_1+C$

$\displaystyle \theta=-2kt_2+C$

Hence:

$\displaystyle 28=-4k(8)+C \Rightarrow \ 28=-32k+C$

$\displaystyle 26=-2k(9)+C \Rightarrow \ 26=-18k+C$

$\displaystyle 2=-14k \Rightarrow k=-\frac{1}{7}$

However, my book says k should be $\displaystyle ln \ 2$. What's going wrong?