Given: The growth rate and a point
[tex]\begin{gathered} rate(r)=0.3 \\ Point1:(4,1.7) \end{gathered}[/tex]To Determine: The point-slope form of the equation
Solution
The general point-slope form a lineal function is given as
[tex]\begin{gathered} Point1:(x_1,y_1) \\ slope:m \\ The\text{ general form is} \\ (y-y_1)=m(x-x_1) \end{gathered}[/tex]Please note that the rate is the same as the slope. Therefore, substituting the given point and rate into the general form
[tex]\begin{gathered} (x_1,y_1)=(4,1.7) \\ m=0.3 \\ Therefore \\ (y-1.7)=0.3(x-4) \end{gathered}[/tex]After 7 years, we have x = 7, therefore, y would be
[tex]\begin{gathered} y-1.7=0.3(x-4) \\ x=7 \\ y-1.7=0.3(7-4) \\ y-1.7=0.3(3) \\ y-1.7=0.9 \\ y=0.9+1.7 \\ y=2.6 \end{gathered}[/tex]Hence, the solution is
y - 1.7 = 0.3(x - 4), 2.6 meters
