Respuesta :
Answer:
[tex]P=-500t+39400[/tex], where t is the number of years since 1995.
Step-by-step explanation:
It is given that the population of a town shown a linear decline in the years 1995-2003.
Let P is the population of the town at time t, where t is the number of years since 1995.
In 1995 the population was 39400 people. In 2003 it was 35400 people. It means the ordered pairs of the function are (0,39400) and (8, 35400).
If a line passes through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], then the equation of line is
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
So, the equation of population function is
[tex]y-39400=\frac{35400-39400}{8-0}(x-0)[/tex]
[tex]y-39400=\frac{-4000}{8}x[/tex]
[tex]y-39400=-500x[/tex]
Add 39400 on both sides.
[tex]y=-500x+39400[/tex]
Substitute y=P and x=t in the above equation.
[tex]P=-500t+39400[/tex]
Therefore, the required equation is [tex]P=-500t+39400[/tex].
