Explanation

(b) According to Newton’s law of cooling
Rate of cooling $\propto$ Temperature difference
$\Rightarrow - \frac{d\theta}{dt} \propto \left( \theta - \theta_{0} \right) \Rightarrow - \frac{d\theta}{dt} = \alpha\left( \theta - \theta_{0} \right)\ \ \lbrack\alpha =$ constant]
$\Rightarrow \int_{\theta_{1}}^{\theta}{\frac{d\theta}{(\theta - \theta_{0})} = - \alpha\int_{0}^{1}{dt\ \Rightarrow \theta = \theta_{0} + \left( \theta_{1} - \theta_{0} \right)e^{- \alpha t}}}$
This relation tells us that, temperature of the body varies exponentially with time from $\theta_{1}$ to $\theta_{0}$
Hence graph (b) is correct