b
(b) According to Newton's law of cooling Rate of cooling \(\propto\) Temperature difference

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

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