Acertain city spans 126,000 square miles. the population of this city is 683,000 people. what is the population density of the city? what is the population density of the city if the population grows to 1,000,000 people?

For you to be able to get the population density you need to divide the population by the size of the area. The formula looks like this:

Population Density = Number of People/Land Area
                               = 683,000/126 square miles 
                               = 5,420 people/square miles 

If it grows to 1,000,000 people the solution is:
Population density = 1M/683,000 square miles
                              = 1.46 people/square miles