Question

The population of a city in 2005 was 18,000. By 2010, the city’s population had grown to 32,800. If the population growth follows a linear model, what is the projected population for 2015?

Answer 1

it grew (32,800 - 18,000) in five years

linear means the same amount of growth over the next five years

Answer 2

you have two ordered pairs, (2005,18000) and (2010,32800)
slope = (32800-18000)/(2010-2005)
= 14800/5 = 2960

so pop = 2960t + b, where t is the year
sub in one of the points, say (2005,18000)
18000 = 2960(2005) + b
b = -5916800

pop = 2960t - 5916800
replace t with 2015 to find pop