The correct answer is option 2, Exosphere. The exosphere is the outermost layer of the Earth`s atmosphere. In this layer, the temperature increases rapidly because there are very few particles present to absorb and retain heat. The few particles that do exist in the exosphere have high kinetic energy and can reach very high temperatures.

On the other hand, the troposphere, which is option 4, is the lowest layer of the Earth`s atmosphere, closest to the surface. In the troposphere, the temperature generally decreases with an increase in altitude.

Therefore, although the temperatures change in different layers of the atmosphere, the exosphere is the layer where the temperature increases rapidly.