Jeff K. answered • 05/06/20

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Hi, Gabrielle:

The question specifies a __linear__ decline. This means the population falls in a __straight line__ from year to year.

So, we need an equation of the from: P(t) = mt + b [where P(t) is the population at year t after 2001]

This equation has 2 unknowns we must find, namely, m and b

From the information given, P(0) = 25,500: 25,500 = m x 0 +b . . . . . . . eqn (1)

and P(10) = 18,200: 18,200 = m x 10 + b . . . . . . . eqn (2)

From eqn (1), we see that: __b = 25,500__

Plug this into eqn (2): 18,200 = 10m + 25,500

-7,300 = 10m

so __m = -730__ [the number of residents lost per year]

Therefore, answer A: the population equation is: __P(t) = -730t + 25,500__

Part B: In 2016, t = 2016 - 2001 = 15 years. Plug this into eqn (3): P(15) = -730 x 15 + 25,500

= __14,550__