In 2007, the population of a town was approximately 35,250. In 2012, the population of the town had decreased to 28,200. Based on a linear model, what will be the approximate population of the town in 2014?

Question

In 2007, the population of a town was approximately 35,250. In 2012, the population of the town had decreased to 28,200. Based on a linear model, what will be the approximate population of the town in 2014?
Ive gotten -7050/2005= -4(rounded) 
then for the answer i got 36228 people but got it wrong please help.

Reiny · Accepted Answer

since it is linear, find the slope of the two ordered pairs that you have:
assume 2007 ----> t = 0
then for 2012 , t = 5

slope = (28200 - 35250)/(5-0) = -1410
(interpretation: the town loses 1410 each year)

so using the point (0,35250)
the equation can be written as
P = -1410t + 35250

so for 2014, t = 7
P = -1410(7) + 35250 = 25380

Since the population is clearly decreasing , your answer of 36228, which was more than what we started with, should have appeared to be illogical to you.