A hot liquid is placed in a large room. The temperature of the...

According to Newton's law of cooling, the rate of loss of heat is directly proportional to the difference in temperature between the body and its surroundings.

$\dfrac{d\theta}{dt} = -k(\theta - \theta_0)$

where $\theta$ is the temperature of the liquid at time $t$, $\theta_0$ is the temperature of the surroundings, and $k$ is a positive constant.

Integrating the above equation, we get:

$\theta = \theta_0 + (\theta_i - \theta_0)e^{-kt}$

where $\theta_i$ is the initial temperature of the liquid.

This equation represents an exponentially decaying curve. The temperature decreases continuously and approaches the surrounding temperature $\theta_0$ asymptotically.

The slope of the curve is negative and its magnitude decreases with time, making the curve concave upwards.

Among the given graphs, curve $a$ represents an exponentially decreasing function that is concave upwards.