Answer:
In 17th year, his income was $30,700.
Step-by-step explanation:
It is given that the income has been increasing each year by the same dollar amount. It means it is linear function.
Income in first year = $17,900
Income in 4th year = $20,300
Let y be the income at x year.
It means the line passes through the point (1,17900) and (4,20300).
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]
The equation of line is
[tex]y-17900=\frac{20300-17900}{4-1}(x-1)[/tex]
[tex]y-17900=\frac{2400}{3}(x-1)[/tex]
[tex]y-17900=800(x-1)[/tex]
[tex]y-17900=800x-800[/tex]
Add 17900 on both sides.
[tex]y=800x-800+17900[/tex]
[tex]y=800x+17100[/tex]
The income equation is y=800x+17100.
Substitute y=30,700 in the above equation.
[tex]30700=800x+17100[/tex]
Subtract 17100 from both sides.
[tex]30700-17100=800x[/tex]
[tex]13600=800x[/tex]
Divide both sides by 800.
[tex]\frac{13600}{800}=x[/tex]
[tex]17=x[/tex]
Therefore, in 17th year his income was $30,700.
