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The population of a small town in central Florida has shown a linear decline in the years 1985-1997. In 1985 the population was 46000 people. In 1997 it was 38080 people.

The population of a small town in central Florida has shown a linear decline in the years 19851997 In 1985 the population was 46000 people In 1997 it was 38080 class=

Respuesta :

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.

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