Question

The density of atmosphere (measured in kilograms/meter3) on a certain planet is found to decrease as altitude increases (as measured from the planet's surface). What type of relationship exists between the altitude and the atmospheric density, and what would the atmospheric density be at an altitude of 1,291 kilometers?

Answer 1

As the question does not really tell you exactly how it decreases, I would say it is probably linearly. So you can make an equation for density, as a function of height, with the starting density as that at the surface, which looks like the equation of a straight line. the 'graph' may help. [the atmosphere on Earth decreases in a more complex way, I don't think the question wants that] (y=mx + b)

Answer 2

Earth's atmosphere has a density distribution that decreases
exponentially, approximately exp(-a h), where h is height above ground. Related to energy: exp(-mgh/kT)