==> $ - \frac{{d\theta }}{{dt}} \propto (\theta - {\theta _0})$

==>$ - \frac{{d\theta }}{{dt}}$=$\alpha \;(\theta - {\theta _0})$ ($\alpha$= constant)

==> $\int\limits_{{\theta _i}}^\theta {\frac{{d\theta }}{{(\theta - {\theta _0})}} = - \alpha \int\limits_0^t {dt} } $

==> $\theta = {\theta _0} + ({\theta _i} - {\theta _0}){e^{ - \alpha \,t}}$

This relation tells us that, temperature of the body varies exponentially with time from ${\theta _i}$ to ${\theta _0}$
Hence graph $(b)$ is correct.