$A$ body cools in a surrounding which is at a constant temperature of $\theta_0$. Assume that it obeys Newton's law of cooling. Its temperature $\theta$ is plotted against time $t$. Tangents are drawn to the curve at the points $P(\theta = \theta_2)$ and $Q(\theta = \theta_1)$. These tangents meet the time axis at angles of $\varphi_2$ and $\varphi_1$,as shown in the figure.

• A
  $\frac{\tan \varphi_2}{\tan \varphi_1} = \frac{\theta_1 - \theta_0}{\theta_2 - \theta_0}$
• B
  $\frac{\tan \varphi_2}{\tan \varphi_1} = \frac{\theta_2 - \theta_0}{\theta_1 - \theta_0}$
• C
  $\frac{\tan \varphi_1}{\tan \varphi_2} = \frac{\theta_1}{\theta_2}$
• D
  $\frac{\tan \varphi_1}{\tan \varphi_2} = \frac{\theta_2}{\theta_1}$