b
$Newton's\,law$ of cooling
$\frac{d \theta}{d t}=-k\left(\theta-\theta_{0}\right)$
$\int_{\theta_{1}}^{\theta} \frac{d \theta}{\theta-\theta_{0}}=-\int_{0}^{t} k d t$
$\ln \left(\theta-\theta_{0}\right)-\ln \theta_{1}=-k t$
$\ln \left(\theta-\theta_{0}\right)=-k t+\ln \theta_{1}$