Gases exhibit certain behaviors given the temperature or pressure of the system. which model displays the change in a gas when the temperature of the gaseous system decreases?

The equation it's very simple and corresponds to the ideal gas model, which is this one:

Explanation:

Gases tend to behave following the mathematic relationship due to the ideal gas formula shown above; where P is the pressure applied to a gas inside a recipient (for example), V is the volume of the recipient where the gas exists (that is the same volume of the gas since any gas tends to fill all the volume of a limited space of the recipient), n is the number of moles and indicates the amount of gas (molecules of gas) inside the recipient and T is the temperature of that particular gas. R is just a constant called the gas constant (). An ideal gas doesn't lose its internal energy over time, so the collision between the particles of the gas are considered perfect elastic collisions; which means that the system gas-recipient is a closed physical system that won't release energy to the surroundings,

Getting back to the actual question after the background: as n and R are constant, the pressure and temperature are directly correlated to each other, consider we assume V can't change; when the T drops, so does the pressure (think of it as the gas contracts itself because is losing excitation from the source of temperature). In other hand, if T increases, the gas will tend to expand itself so it will also increase the pressure (the gas is now colliding a lot inside the recipient because is gaining energy from the source of temperature)

b.

hope this : )

electric field is a function of 1/r^2

yes, the force per unit charge for a point charge is inverse square law.