Question

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.

Answer 1

Given:

(1985,46000)

(1997,38080)

(a)

General linear equation is:

`y=mx+c`

here y represent the population and x represent time so equation is:

`p=mt+c`

`\begin{gathered} \text{slope}=m \\ m=\frac{p_2-p_1_{}}{t_2-t_1} \end{gathered}`

`\begin{gathered} (p_1,t_1)=(1985,46000) \\ (p_2,t_2)=(1997,38080) \end{gathered}`

slope is:

`\begin{gathered} m=(p_2-p_1)/(t_2-t_1) \\ m=(38080-46000)/(1997-1985) \\ m=(-7920)/(12) \\ m=-660 \end{gathered}`

So equation is:

`\begin{gathered} p=mt+c \\ p=-660t+c \end{gathered}`

Point (1985,46000)

`\begin{gathered} p=-660t+c \\ p=46000 \\ t=1985 \\ p=-660t+c \\ 46000=-660(1985)+c \\ c=46000+1310100 \\ c=1356100 \end{gathered}`

So equation is:

`\begin{gathered} p=mt+c \\ p=-660t+1356100 \end{gathered}`

(b)

population in 2000.

`t=2000`

`\begin{gathered} p=mt+c \\ p=-660t+1356100 \\ t=2000 \\ p=-660(2000)+1356100 \\ p=36100 \end{gathered}`

so population in 2000 is 36100.