Question

The population of a small town in central Florida has shown a linear decline in the years 1996-2004. In 1996 the population was 39500 people. In 2004 it was 32140 people.

Answer 1

Given:

`\begin{gathered} (1996,39500) \\ (2004,32140) \end{gathered}`

(a)

General linear equation :

`y=mx+c`

y represent the population (p) and x represent time (t).

so equation is:

`p=mt+c`

slope :

`m=(p_2-p_1)/(t_2-t_1)`

`\begin{gathered} (p_1,t_1)=(1996,39500) \\ (p_2,t_2)=(2004,32140) \end{gathered}`

`\begin{gathered} m=(32140-39500)/(2004-1996) \\ m=(-7360)/(8) \\ m=-920 \end{gathered}`

so equation is:

`\begin{gathered} p=mt+c \\ p=-920t+c \\ (1996,39500) \\ 39500=-920(1996)+c \\ c=39500+(920*1996) \\ c=39500+1836320 \\ c=1875820 \end{gathered}`

so equation is:

`\begin{gathered} p=-920t+1875820 \\ p+920t=1875820 \end{gathered}`

(b)

population in 2008 is:

`t=2008`

`\begin{gathered} p=-920t+1875820 \\ t=2008 \\ p=-920(2008)+1875820 \\ p=28460 \end{gathered}`

population in 2008 is 28460