Answer:
[tex]\begin{gathered} \text{ A. }y-15=5(x-3) \\ \text{ B. }y=\text{ 60 cm} \end{gathered}[/tex]Step-by-step explanation:
This situation can be modeled by a linear equation since it has a constant rate of change. Linear functions are represented in the slope-point form by:
[tex]\begin{gathered} y-y_0=m(x-x_0) \\ \text{where,} \\ m=\text{slope} \\ (x_0,y_0)\rightarrow_{}\text{ given point} \end{gathered}[/tex]The slope can be calculated as:
[tex]m=\frac{y_1-y_0}{x_1-x_0}[/tex]Given the information on the table, we can use the points (3, 15) and (5,25):
[tex]\begin{gathered} m=\frac{25-15}{5-3} \\ m=\frac{10}{2} \\ m=5 \end{gathered}[/tex]A. Then, by the slope-point form we can model the situation:
[tex]\begin{gathered} y-15=5(x-3) \\ \end{gathered}[/tex]B. Now, to predict the height of the plant after 12 months, substitute x=12 into the equation:
[tex]\begin{gathered} y=5x-15+15 \\ y=5x \\ y=5(12) \\ y=\text{ 60 cm} \end{gathered}[/tex]