Given:
(1985,46000)
(1997,38080)
(a)
General linear equation is:
[tex]y=mx+c[/tex]
here y represent the population and x represent time so equation is:
[tex]p=mt+c[/tex]
[tex]\begin{gathered} \text{slope}=m \\ m=\frac{p_2-p_1_{}}{t_2-t_1} \end{gathered}[/tex]
[tex]\begin{gathered} (p_1,t_1)=(1985,46000) \\ (p_2,t_2)=(1997,38080) \end{gathered}[/tex]
slope is:
[tex]\begin{gathered} m=\frac{p_2-p_1}{t_2-t_1} \\ m=\frac{38080-46000}{1997-1985} \\ m=\frac{-7920}{12} \\ m=-660 \end{gathered}[/tex]
So equation is:
[tex]\begin{gathered} p=mt+c \\ p=-660t+c \end{gathered}[/tex]
Point (1985,46000)
[tex]\begin{gathered} p=-660t+c \\ p=46000 \\ t=1985 \\ p=-660t+c \\ 46000=-660(1985)+c \\ c=46000+1310100 \\ c=1356100 \end{gathered}[/tex]
So equation is:
[tex]\begin{gathered} p=mt+c \\ p=-660t+1356100 \end{gathered}[/tex]
(b)
population in 2000.
[tex]t=2000[/tex]
[tex]\begin{gathered} p=mt+c \\ p=-660t+1356100 \\ t=2000 \\ p=-660(2000)+1356100 \\ p=36100 \end{gathered}[/tex]
so population in 2000 is 36100.
