Given:
[tex]\begin{gathered} (1996,39500) \\ (2004,32140) \end{gathered}[/tex]
(a)
General linear equation :
[tex]y=mx+c[/tex]
y represent the population (p) and x represent time (t).
so equation is:
[tex]p=mt+c[/tex]
slope :
[tex]m=\frac{p_2-p_1}{t_2-t_1}[/tex]
[tex]\begin{gathered} (p_1,t_1)=(1996,39500) \\ (p_2,t_2)=(2004,32140) \end{gathered}[/tex]
[tex]\begin{gathered} m=\frac{32140-39500}{2004-1996} \\ m=\frac{-7360}{8} \\ m=-920 \end{gathered}[/tex]
so equation is:
[tex]\begin{gathered} p=mt+c \\ p=-920t+c \\ (1996,39500) \\ 39500=-920(1996)+c \\ c=39500+(920\times1996) \\ c=39500+1836320 \\ c=1875820 \end{gathered}[/tex]
so equation is:
[tex]\begin{gathered} p=-920t+1875820 \\ p+920t=1875820 \end{gathered}[/tex]
(b)
population in 2008 is:
[tex]t=2008[/tex]
[tex]\begin{gathered} p=-920t+1875820 \\ t=2008 \\ p=-920(2008)+1875820 \\ p=28460 \end{gathered}[/tex]
population in 2008 is 28460
