The population of a city in 2005 was 18,000. by 2010, the city’s population had grown to 45,000. economists have determined that the population growth follows an exponential model. if they are correct, what is the projected population for 2015?

Since the population growth follows a linear model, we can let x be the year and y be the population and further let
x1=2005x2=2010y1=18,000y2=32,800
After which, we can use the two-point form, given as (y2-y1)/(x2-x1)=(y-y1)/(x-x1), to find the linear equation that represents the population growth. Thus, 
(32,800-18,000)/(2010-2005)=(y-18,000)/(x-2005)14,800(x-2005)=5(y-18,000)14,800x-29,674,000=5y-90,0005y=14,800x-29,674,000+90,0005y=14,800x-29,584,000y=2960x-5,916,800
Thus, we can now calculate for the projected 2015 population. Substitute 2015 to x in the above equation and we have 47,600.