In 2006, the population of a certain country per square mile of land was 81. in 2014, the persons per square mile was 85.24. assume the relationship between years, x, and persons per square mile, y, is a linear relationship

Assuming a linear relationship we can express the population density as a function of the year.

d(y)=m(y-2006)+b  

m=(d2-d1)/(y2-y1)=(85.24-81)/(2014-2006)

m=4.24/8

m=0.53

d(y)=0.53(y-2006)+b, using point (2014,85.24) we can solve for b

85.24=0.53(8)+b

85.24=4.24+b

81=b so

d(y)=0.53(y-2006)+81  (so this a the population density (persons per mi^2 as a function a year)