A town's population has been growing linearly. In 2004 the population was 6200 . By 2009 the population had grown to 8100 . Assume this trend continues.

We begin by finding the annual change in population. From 2004 to 2009 (a 5-year period), the population increased from 6200 to 8100. That is, the increase was   8100 − 6200 = 1900 people. Since this increase happened over 5 years, the yearly increase is   1900 ÷ 5 = 380 people per year. Now, let t represent the actual year. We can model the population P(t) with a linear function in the form   P(t) = P₀ + r(t − t₀), where P₀ is the population in the starting year t₀ and r is the annual rate of change. If we take t₀ = 2004 and P₀ = 6200, then the model becomes   P(t) = 6200 + 380(t − 2004). This function satisfies the given information: • For t = 2004, P(2004) = 6200 + 380(2004 − 2004) = 6200. • For t = 2009, P(2009) = 6200 + 380(2009 − 2004) = 6200 + 380×5 = 6200 + 1900 = 8100. Thus, assuming the current trend continues, the town’s population in any year t is given by   P(t) = 6200 + 380(t − 2004). For example, if you wish to predict the population for 2015, substitute t = 2015 into the model:   P(2015) = 6200 + 380(2015 − 2004)        = 6200 + 380×11        = 6200 + 4180        = 10380. This is the prediction based on the linear growth trend.