The Arithmetic density tell us about the total number of people divided the total land area in a country.Us as geographers care for this to compare the number of people living on a given piece of land in different regions of the world.
Countries use the physiological density to see if the land is suitable for agriculture. Geographers care for this so they can understand the capacity of the land yield enough food for the needs of the people.
Countries use the agriculture density to compare the amount of food each produce having the same physiological densities. Geographers care for this because they can examine economic differences between countries.